Session BP9: Poster Session I: MHD, Two-Fluid, Chaos, and Nonlinear Interactions; NSTX Spherical Torus; Magnetic Confinement Simulation and Modeling; MHD Equilibrium, Stability, and Energetic Particle Effects

Characterization of Flow and Ohm's Law in the Rotating Wall Machine

The rotating wall machine is a linear screw-pinch built to study the role of different electromagnetic boundary conditions on the Resistive Wall Mode (RWM). Its plasma is created by an array of electrostatic washer guns which can be biased to discharge up to 1 kA of current each. Individual flux ropes from the guns shear, merge, and expand into a 20 cm diameter, $\sim 1$ m long plasma column. Langmuir (singletip) and tri-axial B-dot probes move throughout the column to measure radial and axial profiles of key plasma parameters. As the plasma current increases, more $H_2$ fuel is ionized, raising $n_e$ to $5 \times 10^{20}$ m$^{-3}$ while $T_e$ stays at a constant 3 eV. The electron density expands to the wall while the current density ($J_z$) stays pinched to the central axis. ${\bf E} \times {\bf B}$ and diamagnetic drifts create radially and axially sheared plasma rotation. Plasma resistivity follows the Spitzer model in the core while exceeding it at the edge. These measurements improve the model used to predict the RWM growth rate.   

Stabilization of the Line-Tied Resistive Wall Mode by a Rotating Conducting Wall

The Rotating Wall Machine is testing the hypothesis that the Resistive Wall Mode (RWM) can be stabilized by rotating conducting walls. These walls allow stabilizing image currents to persist despite finite wall resistivity. A rotating wall has been constructed that has demonstrated rotation speeds up to 280 km/h, which corresponds to a magnetic Reynolds number ($R_m$) of 5. Previous experiments have identified the RWM by varying the device wall and noting that the growth rate of the mode scaled with the wall resistive diffusion time. Observations also indicated that this mode was locked to the wall and external in character. With the rotating wall it is expected that at the highest speeds 25\% more plasma current can be driven while maintaining stability to the RWM. For RWM unstable plasmas, it is expected that as the wall velocity increases the growth rate of the RWM will decrease. Design and preliminary data with this wall will be presented. Flow measurements using a Mach probe and their relationship to MHD stability will also be presented.   

Measurements of Line-tied Kink Eigenfunction in the Rotating Wall Machine and Comparison to Simulation

The internal kink instability in the Rotating Wall Machine has an ideal character, but also exhibits reconnection events that periodically flatten the current profile and change the magnetic topology. A scanning, 3-axis magnetic probe has been used to measure the internal equlibrium and fluctuating magnetic fields. Using shot-to-shot averaging, 2D profiles (R,Z) of the plasma can be measured via an an axially scanning traverse. Internal mode structure has been determined through multiple-shot correlation analysis. The line-tying conditions in the machine are examined through the structure of the magnetic field. Finally, using equilibrium measurments of $n_e$, $T_e$, and $J$ as inputs, the line-tied kink mode has been studied numericaly using the NIMROD code. Linear and nonlinear simulation results are presented and compared to experiment.   

Ion Flows in Quasi Equilibrium Magnetized Plasmas

In an ionized gas, conductivity perpendicular to a magnetic field generally is reduced over its free-space value by the factor [1+(\textit{$\omega $}$_{c}$\textit{/$\nu $})$^{2}$] where \textit{$\omega $}$_{c}$ and \textit{$\nu $} are the electron cyclotron and collision frequencies respectively. On the other hand, in a cylindrical Z-pinch plasma in a minimum-total-energy equilibrium with the minor radius just larger than the electron skin depth, $[m_{e}$\textit{/($\mu $}$_{o}n_{o}e^{2})]^{1/2 }$, forces on electrons and ions include not only magnetic and thermal but an electrostatic force resulting from unequal electron and ion charge distributions. Except for the force driving the current, the resulting net force is zero. As a result the magnetic field does not cause a reduction in the conductivity even though the velocities of both electron and ion fluid particles are perpendicular to the magnetic field, In this case electrons dominate the current. On the other hand, if the equilibrium minor radius is on the order of the ion skin depth, the electron current is impeded by the magnetic field but the ion current is not, consequently ions dominate. Such ion current appears to be present in Venus flux ropes, filaments during the rundown phase in the plasma focus, reverse field configurations, and other magnetic systems.   

Applications of the Two-Fluid Plasma Model to Simulate Instabilities with and without Background Magnetic Fields

The two-fluid plasma model consists of the $5$-moment equations to describe the ion and electron fluids. This provides a continuity, momentum, and energy equation for each of the ion and electron fluids. Maxwell's equations are used to evolve the electric and magnetic fields. Washington Approximate Riemann Plasma (WARPX) code is a finite element code based on the two-fluid plasma model which uses the Runge-Kutta discontinuous Galerkin method. The two-fluid plasma model is applied to simulate instabilities with and without background magnetic fields. A Z-pinch is simulated to study the development of two-fluid small-scale instabilities with $k\rho_i\sim 1$. The small-scale instabilities lead to electromagnetic fluctuations and drift-turbulence. In the absence of background magnetic fields, the development of a Rayleigh-Taylor instability is simulated in a stratified plasma which has potential applications in inertial confinement configurations and astrophysics. The effect of two-fluid physics on the nonlinear evolution of the Rayleigh-Taylor instability is explored.   

Axial Transport with free plasma-neutral end-boundary in Enormous Toroidal Plasma Device (ETPD): ``The End of the Plasma''

Axial transport of particles, momentum, and heat in a magnetized, quiescent ($\delta $n/n $<$5{\%}), current-free plasma with a free end-boundary terminating on a neutral gas are studied. The experiment is done on the ETPD at UCLA, a large toroidal device (major radius = 5 m, 2 m wide, 3 m tall) with a pulsed (1 Hz) DC plasma discharge (t$_{d} \quad <$ 100 ms) with a toroidal (B$_{t} \quad <$ 320 G) and a vertical (B$_{v} \quad <$ 8 G) magnetic field. An 18 cm x 18 cm LaB$_{6}$ plasma source creates a helical plasma with length L $<$ 120 m, n$_{e} \quad <$ 3x10$^{13}$ cm$^{-3}$, T$_{e} \quad <$ 20 eV, and T$_{i} \quad <$ T$_{e}$. The LaB$_{6}$ source injects heat and momentum in a beam of primary electrons (energy $<$ 400 eV) that ionize a neutral gas and thermalize in the plasma. The plasma length is set by the primary electron energy and flux, neutral fill pressure, and B$_{t}$ with the plasma able to be fully ``detached'' axially from any wall. Radial plasma profiles and losses are measured, compared to models, and balanced against the input power to predict the plasma length. Also, the properties of the axial plasma-neutral boundary as a sink for particles by 3-body recombination, heat loss by thermalization with neutrals, and momentum loss by ion-neutral collisions are investigated. Work funded by the Department of Energy and National Science Foundation.   

Computational Algorithm for the Multi-Fluid Plasma Model - WARPX

An algorithm is developed for the multi-fluid plasma model derived from moments of the Boltzmann equation, which only assumes local thermodynamic equilibrium within each fluid, e.g. ion and electron fluids for the two-fluid plasma model. Physical parameters determine the importance of the two-fluid effects: electron to ion mass ratio $m_e/m_i$, ion skin depth $\delta_i$, and ion Larmor radius $r_L$. Asymptotic approximations of the two-fluid plasma model, Hall-MHD, lead to an unbounded Whistler wave that requires artificial dissipation. No unbounded waves exist in the two-fluid plasma model. Adding additional fluids, e.g. neutrals, is a simple extension of the model. The computational algorithm simulates plasma dynamics with a finite element (discontinuous Galerkin) method that uses an approximate Riemann solver to compute the fluxes of the fluids and electromagnetic fields at the computational cell interfaces. The algorithm is validated with several test problems including the GEM challenge magnetic reconnection problem and the generation of dispersive plasma waves which are compared to analytical dispersion diagrams. Solutions of Z-pinch and FRC configurations are presented.   

Plasma Sheath Modeling Using The Three Fluid Plasma Model

There has been renewed interest in the use of plasma actuators for high speed flow control applications. In the plasma actuator, current is driven through the surrounding weakly ionized plasma to impart control moments on the hypersonic vehicle. Accurate modeling of plasma sheath physics is of particular importance for the plasmas found in high speed flight applications. This study employs the three-fluid (electrons, ions, neutrals) plasma model as it allows the capture of electron inertial effects without the unbounded whistler wave that accompanies Hall MHD, as well as energy and momentum transfer between the charged and neutral species. Previous investigations have typically assumed an electrostatic electric field. This work includes the full electrodynamics. Floating potential sheath formation is investigated initially. We then present a method of voltage control that allows for control of the sheath. The resulting boundary scheme, in conjunction with the use of the purely hyperbolic Maxwells equation set, will be reviewed and the results in 1D and 2D discussed. Finally the outlook for incorporating transport will be presented.   

Selective decay in a long cylindrical geometry in SSX

A helical, minimum-energy relaxed plasma state has been observed in a long cylindrical volume. The cylinder is long enough (L/R = 13) so that the predicted minimum energy state is a close approximation to the infinite cylinder solution. The plasma is injected at $v \ge 50$~km/s by a coaxial magnetized plasma gun located at one end of the cylindrical volume. The relaxed state is rapidly attained in 1--2 axial Alfv\'{e}n times after initiation of the plasma. Magnetic data is favorably compared with an analytical model. Magnetic data exhibits broadband fluctuations of the measured axial modes during the formation period. The broadband activity rapidly decays as the energy condenses into the lowest energy mode, which is in agreement to the minimum energy eigenstate of $\nabla \times \vec{B} = \lambda \vec{B}$. Merging experiments are planned and additional data will be presented if available.   

Highlights of the Cambridge Gyrokinetics Program: A Personal Perspective

A four-week Program/Workshop on Gyrokinetics in Laboratory and Astrophysical Plasmas (organized by W. Dorland, S. Nazarenko, and A. Schekochihin) occurred in Cambridge, UK, during July 19 -- August 13, 2010. Topics included gyrokinetic (GK) phase-space turbulence, sheared GK turbulence, kinetic reconnection, edge GKs, and approaches to global full-$f$ GK simulations. Key results and outstanding problems that were identified will be summarized from a personal perspective. The material is intended to provide a snapshot of the state-of-the-art in modern GK research and to foster discussion on future directions.   

Gyrokinetic analysis of tearing modes in a collisionless plasma

The linear and nonlinear dynamics of tearing instabilities in a collisionless plasma are investigated analytically using a gyrokinetic description. The effects of Landau and $\rm \nabla B$ resonances on the linear characteristics of $\Delta^{\prime} $-driven tearing modes are discussed by including short wavelength variations across the confining magnetic field and long wavelength variations along the field. For a simple case when electrons are adiabatic and ions are fluid-like, the solutions of dispersion relations are obtained for modewidths, $\rm x_w$, lying between electron and ion excursion lengths, namely, $\rm X_{e,i}$, where $\rm X_{e,i} = \omega L_s/(k_{y} v_ {e,i})$, $\rm k_y$ is the wavenumber, $\rm L_s$ is the magnetic shear length, and $\rm v_{e,i}$ represent electron and ion thermal speeds. It is shown that electron Landau damping effect can drive the tearing mode unstable with growth rate proportional to $(\Delta^{\prime})^{1/2}$. For this mode, it is further shown that the effects of compressional mode coupling and finite Larmor radius can combine to have a slightly stabilizing effect. In another physical situation, it is demonstrated that the electron $\rm \nabla B$ resonance effect can significantly destabilize the gyrokinetic tearing mode with growth rates varying as fractional powers of $\Delta^{\prime}$ and $\rm k_y$. The nonlinear implications of these effects are investigated by deriving an appropriate Rutherford equation for the magnetic island evolution.   

Gyrokinetic simulations of microtearing instability

Microtearing modes driven unstable by electron temperature gradients, may account for the anomaly of electron transport in fusion devices. Since microtearing instabilities are collisional mode ($\nu/\omega_{\ast}>1$; $\nu$ and $\omega_{\ast}$ are the collision and diamagnetic drift frequencies of the electron), these modes should be stable in conventional tokamaks. However, recently, these modes can be the most unstable mode in current spherical tokamaks in which plasma parameters are quite different from conventional tokamaks. We present numerical results of microtearing instability simulations using the \texttt{AstroGK} astrophysical gyrokinetics code. We have successfully reproduced the linear growth of the instability predicted by the theory. We also discuss nonlinear saturation, and electron transport induced by this mechanism.   

On the road to the Hamiltonian formulation of gyrokinetic theory

The Hamiltonian formulation of a general set of field equations is expressed in terms of a Hamiltonian functional and a Poisson- bracket structure involving functional derivatives with respect to dynamical fields. The Hamiltonian functional is normally constructed as the energy functional following a procedure outlined by Pfirsch and Morrison [1], which explicitly introduces polarization effects. The Poisson bracket must satisfy the standard antisymmetry and Leibniz properties as well as the Jacobi identity. We present work in progress on the Hamiltonian formulation for the guiding-center Vlasov-Maxwell equations (without redundant variables), as a prelude to the formulation for the gyrokinetic Vlasov-Maxwell equations [2].\\[4pt] [1] D. Pfirsch and P.J. Morrison, Phys. Rev. A \textbf{32}, 1714 (1985). \newline [2] A.J. Brizard and T.S. Hahm, Rev. Mod. Phys. \textbf{79}, 421 (2007).   

A General Theory for Gauge-Free Lifting

Given a Hamiltonian set of orbit equations, defined on a phase space of arbitrary dimension, with `forces' that depend explicitly on given electric and magentic fields and possibly all of their derivatives, how does one \underline{lift} to a Hamiltonian kinetic theory coupled to Maxwell's equations? A general theory that answers this question will be presented. The theory produces magnetization and polarization effects in Maxwell's equations via a noncanonical Poisson bracket that generalizes that for the Vlasov-Maxwell system\footnote{P.J.~Morrison, Phys.\ Lett.\ {\bf 80A}, 383 (1980); AIP Conference Proceedings {\bf 88}, 13 (1982); J.~Marsden and A.~Weinstein, Physica {\bf 4D}, 394 (1982).}. Several examples will be treated, including the generalized guiding-center kinetic theory of Pfirsch and the author\footnote{D. Pfirsch and P.~J.~Morrison, Phys.\ Rev.\ \textbf{32A}, 1714 (1985); Phys.\ Fluids \textbf{3B}, 271 (1991).}, which relies on the introduction of redundant variables via Dirac constraint theory. Theories without the redundant variables are also being investigated\footnote{A.\ Brizard et al., adjacent poster; P.J.~Morrison and M. Vittot, research in progress.}.   

Gyrokinetic Statistical Absolute Equlibrium and Turbulence

A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence [T.-D. Lee, ``On some statistical properties of hydrodynamical and magnetohydrodynamical fields,'' Q. Appl. Math. 10, 69 (1952)] is taken to study gyrokinetic plasma turbulence. We keep a finite set of Fourier modes of the collisionless gyrokinetic equations and calculate the equilibrium statistics. A new feature is that the integrations over the distributions are functional integrals because of the extra dependence on velocity in gyrokinetics. For the case of two space and one velocity dimension with $N$ velocity grid points (where $N+1$ quadratic invariants are conserved), we find the negative temperature states, corresponding to condensation of the generalized energy into the lowest modes. This indicates a generic feature of inverse energy cascade. Comparisons are made with some classical results, such as those of Charney-Hasegawa-Mima. There is a universal shape for statistical equilibrium of gyrokinetics in three space and two velocity dimensions with one conserved quantity. Possible physical relevance to turbulence, such as zonal flows and a critical balance hypothesis are also discussed.   

Finite Beta Stabilization of Microinstabilities

A new split-weight perturbative particle simulation scheme for finite-$\beta$ plasmas is presented. The scheme is an improvement over the original split-weight scheme [W. W. Lee {\it et. al}, Phys. Plasmas {\bf 8}, 4435 (2001)], which splits the perturbed particle response into adiabatic and non-adaibatic parts. In the new scheme, by further separating out the non-adaibatic response of the particles associated with the quasi-static bending of the magnetic field lines in the presence of background inhomogeneities of the plasma, we are able to demonstrate the finite-$\beta$ stabilization of drift waves and ion temperature gradient modes using a simple gyrokinetic particle code based on realistic fusion plasma parameters. However, for $\beta m_i / m_e \gg 1$, it becomes necessary to use the electron skin depth as the grid size of the simulation to achieve accuracy in solving the resulting singular perturbation equations, where the highest derivative term is multiplied by a smallness parameter. This conclusion is different from the prevailing wisdom that the numerical difficulty in simulation kinetic shear-Alfv\'{e}n physics comes from the so-called Ampere cancellation. The proposed scheme is most suitable for studying finite-$\beta$ physics in general geometry using straight field line coordinates. The work is supported by DoE Contract NO. DE-AC02-09CH11466.   

Experimental verification of dynamics modulation in a periodically-driven neon glow discharge plasma

Two ionization wave modes in a driven neon glow discharge alternate as the dominant mode as their response to the driving force alternates between spatiotemporal and temporal periodic pulling. This phenomenon, termed \emph{dynamics modulation}, was first noted by Koepke, Weltmann, and Selcher [1], who saw two limited but representative cases and proposed a mechanism [2] by which it occurs. Dynamics modulation is reproduced experimentally in a neon glow discharge plasma. The system is periodically driven near a non-dominant mode using a narrow-band ring dye laser tuned to a wavelength near the metastable neon transition at 588.35 nm. A spatially-fixed photodiode with a narrow band filter that selectively passes the primary neon spectral line at 640 nm is used to acquire the time series of luminosity oscillations. These experimental data are used to verify the proposed mechanism and explore the resulting implications for spontaneous unidirectional mode transitions that occur with a change in discharge current.\\[4pt] [1] M. E. Koepke, K.-D. Weltmann, and C. A. Selcher, Bull. Am. Phys. Soc. {\bf 40}, 1716 (1995).\\[0pt] [2] K. -D. Weltmann, M. E. Koepke, and C. A. Selcher, Phys. Rev. E {\bf 62}, 2773, (2000).   

Heating and Turbulence from Magnetic Reconnection, Kinetic Alfven Waves and Whistler Waves in the Solar Corona

Theory and simulations are used to investigate the expected heating and reconnection rates due to tearing modes and kinetic Alfv\'{e}n waves (KAW) in configurations with magnetic islands and flux tube loops of various heights/diameters and collisionality regimes. A simple nonlinear electron scale magnetic reconnection model for the magnetic flux and electrostatic potential dynamics is used, as detailed in W. Horton, J.-H. Kim, and F. Militello, Physics of Plasmas {\bf 14}, 012902 (2007). Collisional terms, electron inertia dispersion and ion polarization currents are included in the dynamical equations. Whistler waves are excited by the small scale dynamics around the X-points, which are investigated with nonlinear wave equations for heating, acceleration and energy transport. Energy densities and Alfv\'{e}nic Poynting fluxes are evaluated. The fractions of the released magnetic energy that goes into plasma flows, plasma heating and radiation are estimated. This analysis informs solar corona heating theories.   

Parallel Electric Field and Particle Acceleration in Oblique Magnetosonic Shock Waves

The electric field parallel to the magnetic field, $E_\parallel$, in nonlinear magnetosonic waves is studied with theory and particle simulations, and its results are applied to the investigation of the effect of $E_\parallel$ on particle acceleration in shock waves. In the ideal MHD, $E_\parallel$ is zero, and it was generally thought that $E_\parallel$ was quite weak. Our studies, however, show that it can be strong in nonlinear magnetosonic waves. In a shock wave with its amplitude $\epsilon \sim O(1)$, the magnitude of the integral of $E_\parallel$ along the magnetic field, $F=-\int E_\parallel ds$, is given as $eF \sim \epsilon (m_i v_A^2 + \Gamma _e T_e)$, where $\Gamma _e$ is the specific heat ratio. Furthermore, particle motions in three acceleration mechanisms are calculated with two different test particle methods: In the first method, the total electric field {\boldmath $E$} is used in the equation of motion, while in the second one, $E_\parallel$ is omitted. Comparison of these calculations confirms that $E_\parallel$ is unimportant in the incessant acceleration of relativistic ions. However, $E_\parallel$ is essential for the acceleration of trapped electrons and for the acceleration of positrons along the magnetic field.   

Drift turbulence driven shear flow study in a laboratory plasma

The nonlinear spectral energy transfer rates between large-scale shear flows and drift wave turbulence were directly measured in a linear plasma device CSDX (Controlled Shear Decorrelation Experiment) using a recently developed technique [1]. The results clearly show a net kinetic energy transfer from turbulence with intermediate frequencies ($\sim $10kHz) to shear flows with low frequencies ($<$1kHz), thus directly confirm the turbulence-driven mechanism of shear flows. In addition, a combined study using Langmiur probe arrays and fast visible light imaging strongly supports a vortex driven physics picture for the observed nonlinear energy transfer. And it shows that the sheared zonal flow is sustained by the emission of drift vortices in the central plasma which then propagate in a spiral trajectory, approach the shear layer, and then merge into the sheared flow, thereby transferring their momentum and kinetic energy to it. Similar mechanisms likely operate at the boundary of tokamak plasmas and should contribute to shear flow amplification and intrinsic rotation in these devices.\\[4pt] [1] M. Xu et al, Phys. Plasmas \textbf{16} 042312 (2009).   

Induced Nonlinear Scattering of Magnetospherically Reflecting Whistlers

Whistler waves regulate the energetic electron population in the magnetosphere through pitch angle scattering of resonant electrons. Sources of whistlers in the lower magnetosphere ($L\sim2-3$ ) include, e.g., lightening discharges, VLF transmitters, and unstable particle distributions. Once the whistler waves are generated, they are maintained in an effective cavity around the lower-hybrid resonant surface where the waves are dissipated. Before the waves are dissipated they pitch angle scatter the resonant electrons. We demonstrate that when the energy density of whistlers exceeds a threshold, which occurs at $\delta B=30-50$ pT , the process of nonlinear induced scattering by thermal electrons [1] dominates both electron-ion collisional damping and linear Landau damping due to superthermal electrons [2]. This occurs primarily by scattering of waves before the wave-packet settles down on a lower-hybrid surface (where the wave is damped). Consequently, 1) the lifetime of whistler wave turbulence is increased from seconds to 10s of seconds, 2) the whistler wave packets spend more time away from the lower-hybrid surface and thus interact more with energetic electrons [1]. Thus the lifetime of energetic electrons is reduced due to the induced nonlinear scattering of whistler waves. [1] Ganguli et al., PoP, 17, 052310 (2010), [2] Innan et al., JGR, 108, 1186 (2003).   

Studies of HF-induced Strong Plasma Turbulence at the HAARP Ionospheric Observatory

High power HF transmitters may induce a number of plasma instabilities in the interaction region of overdense ionospheric plasma. We report results from our recent experiments using over one gigawatt of HF power (ERP) to generate and study strong Langmuir turbulence (SLT) and particle acceleration at the HAARP Observatory, Gakona, Alaska. Among the effects observed and studied in UHF radar backscatter are: SLT spectra including the outshifted plasma line or free-mode, appearance of a short timescale ponderomotive overshoot effect, collapse, cascade and co-existing spectra, control of artificial field-aligned irregularities (AFAI), the aspect angle dependence of the plasma line spectra, and suprathermal electrons. Mapping the intensity of SLT versus pointing angle, we have discovered a number of regions of strong interaction displaced from the primary HF interaction region. Stimulated electromagnetic emission (SEE) measurements complement radar measurements. Experimental results are compared to previous high latitude experiments and predictions from recent modeling efforts.   

Anomalous Resistivity Generated By Ion Acoustic Instabilities in Weakly Collisional Plasmas

The anomalous resistivity associated with the current-driven ion-acoustic instability has been proposed as a mechanism for magnetic reconnection, and other forms of transport and dissipation. Recently, it has been shown that the underlying eigenmode spectrum of weakly collisional plasmas in the limit of small collisions is fundamentally different from that of collisionless plasmas. This raises the question of how quasilinear predictions of anomalous resistivity derived from the Vlasov equation differ from those obtained from a weakly collisional theory, even in the limit of zero collisions. We compare the predictions of quasilinear theory with simulation results obtained from a code which integrates the kinetic Lenard-Bernstein equation coupled to the Poisson equation. In contrast with recent results that cast doubt on the validity of the classical estimates (obtained by A. Galeev and R. Sagdeev), we find that our results agree well with the classical estimates, even in the presence of weak collisions. Deviations from the classical quasilinear estimates occur in the nonlinear regime when the application of quasilinear theory is open to question. Comparisons are made with other numerical studies in the collisionless regime, including predictions for the saturated electric field.   

Linear and Nonlinear Whistler Wave Propagation in the Magnetosphere Based on Plasma Density Models from IMAGE Spacecraft Data

From the radio plasma imager on the IMAGE satellite, spatial profiles of electron density in the inner magnetosphere were constructed [B.W. Reinisch {\it et al}, Geophys. Res. Lett., {\bf 28}, 1167 (2001)]. We use these profiles and the dipolar magnetic field model to analyze the propagation of whistler waves. We compute the dispersion characteristics of wave packets from the 2D $\omega(kx,kz,n, B)$ dispersion function, showing wave energy focusing into low phase velocity regions. We add model growth rates from S. Sazhin, {\it Whistler-mode waves in a hot plasma} (Cambridge U. Press, Cambridge, 1993) and nonlinear terms from Horton {\it et al} [W. Horton {\it et al}, Nonlinear Dynamics of the Electromagnetic Ion Cyclotron Structures, Firehose and Whistlers, preprint, Nonlin. Processes Geophys.] to determine saturation levels of whistler chorus waves and associated coherent structures. We explore NLS, DNLS and vortex models, consistent with experiments by Stenzel {\it et al} [R.L. Stenzel {\it et al}, Plasma Phys. Control. Fusion {\bf 50} 074009 (2008)].   

Electrostatic solitary waves in an ultra-relativistic degenerate quantum plasma

Electrostatic solitary waves in an ultra-relativistic degenerate quantum plasma sphere have been investigated by the reductive perturbation method. The modified Korteweg de-Vries equation has been derived, and its numerical solutions have been analyzed to study the basic features of spherical electrostatic solitary structures in such an ultra-relativistic degenerate quantum plasma sphere. The implications of our results in some interstellar objects, particularly in white dwarf, have been briefly discussed.   

Solitary Wave Structures in Inhomogeneous Magnetized Plasma having Trapped Electrons and Dust Grains

An ordinary plasma which contains positive ions and electrons generally supports the propagation of compressive solitons (density hill type structure). However, if negative ions are also present in the plasma, rarefactive solitons (density dip type structure) can occur. The soliton structure can trap plasma particles and convect them over large distances. Hence, they can contribute to the transportation of anomalous particles and the energy from one region to another in laboratory, astrophysical and space related plasmas. In most of the real situations, some dust particles are always present in the plasma that may get negatively charged. Therefore, we investigate here the nonlinear solitary wave structure in an inhomogeneous magnetized plasma that has trapped electrons and negatively charged dust grains. Our calculations show that two types of modes are possible in the plasma which correspond to the propagation of solitary structures under certain conditions. These conditions are obtained and the propagation characteristics of the solitary waves are investigated under the effect of charge of dust grains, magnetic field, obliqueness of the wave propagation, etc.   

Two-dimensional Bernstein-Greene-Kruskal Modes in a Magnetized Plasma: Exact Solutions and Particle-in-Cell Simulations

We present here a new analysis in constructing two-dimensional Bernstein-Greene-Kruskal (BGK) modes in a magnetized plasma with finite magnetic field strength. The original method of constructing these modes [Ng, Bhattacharjee, and Skiff, Phys. Plasmas 13, 055903 (2006)], which satisfy the exact electromagnetic Vlasov-Poisson-Ampere system, requires solving them iteratively. An interesting property of these modes is that they can have a strong magnetic component for large electron thermal velocity. Exact solutions are presented using a new method that solves more directly without this iterative step for any electron thermal velocity. We will also present preliminary results on simulating these modes using Particle-in-Cell (PIC) simulations, which is important in studying the stability of these modes.   

Low Velocity Ion Stopping in a Collisional Magnetized Plasma

We investigate low velocity ion slowing down (LVISD)in a collisional and magnetized plasma. Ion stopping power is calculated through the linear response theory (LRP) based on a dielectric function approach. Collisions which monitore the damping of plasma excitations are accounted for with a number-preserving relaxation time approximation within LRP. Damping effects are highlighted by comparing analytical and numerical results for pointlike collisions and also zero damping. Kinetic [1] results are also contrasted to recent hydrodynamic [2] ones for LVISD parallel and orthogonal to the steady and applied magnetic field of arbitrary magnitude. \\[4pt] [1] H.B.Nersisyan et al,PRE 61,7022(2000)\\[0pt] [2] C.Deutsch and R.Popoff,PRE 78,056405(2008)   

On flow structures and the hierarchy of shears

We investigate the consequences of mean profile dynamics in flux-driven gyrokinetics. We report the emergence of a novel flow structure in plasma turbulence, which we call the ``ExB staircase.'' This structure connects to strong, standing corrugations in the plasma profiles, which is not related to rational q surfaces. We also show that the ExB shear associated to these mean profile corrugations is strongly dominant as compared to the usually-invoked zonal flow shear. Discussion of the dynamics of mean profiles (i) as another channel for turbulence regulation, missing in ``usual'' gyrokinetic approaches, (ii) its connection with turbulent stresses and the transport of potential vorticity, its link (iii) to the observed flow patterns and (iv) to the question of locality vs non-locality in transport is presented.   

Relativistic Laser-Plasma Interactions in the Quantum Regime

We investigate the nonlinear interaction between a relativistically strong laser wave and a plasma in the quantum regime. The collective behavior of electrons is modeled by the Klein-Gordon equation, which is coupled nonlinearly to the electromagnetic wave equation and Poisson's equation for the electromagnetic vector and scalar potentials. This allows us to study the nonlinear interaction between an arbitrarily large amplitude electromagnetic wave and a quantum plasma. We study the importance of the quantum diffraction on the nonlinear dynamics of the system. The study has importance for the nonlinear interaction between super-intense X-ray laser light and solid density plasma, where quantum effects are important.   

Force-Free and Multifluid Relativistic Plasmas

We investigate two topics in Relativistic Astrophysics: ``Force-Free'' Evolution with boundary pressure: In the large sigma limit, the evolution of magnetic fields around a rotating accretion disk are approximately force free. Field lines are wrapped up by the disk and expand outward with ExB velocity. We simulate this, retaining pressure terms far from the disk, and investigate how the morphology and evolution of the fields are changed by external pressure. ``Relativistic Multi-fluid Plasmas'': We describe a ``minimal coupling'' model of charged relativistic (both bulk and thermal motion) magnetofluids, and derive a minimization principle for relaxed states. Applications to pair plasmas in relativistic pulsar striped winds are discussed.   

Magnetization of electron-positron plasmas by Laguerre-Gaussian light beams carrying orbital angular momentum

It is shown that the relativistic ponderomotive force of intense circularly polarized Laguerre-Gaussian electromagnetic beams can create the space charge electric field which sets differential motions of the electrons and positrons in an electron-positron plasma. The resulting plasma current, in turn, creates quasi-stationary magnetic fields due to Faraday's law. The magnetization by different Laguerre-Gaussian modes carrying orbital angular momentum are investigated.   

GEANT4 Monte Carlo Simulation of Pair Creation Using Petawatt Lasers

Irradiating high-Z targets such as gold with ultra-intense lasers creates electron-positron pairs. First the laser heats the target surface and creates a plasma. The laser then accelerates electrons to relativistic energies out of the plasma and through the target, creating pairs emerging on the opposite side. The positron density in the outgoing plasma created by this procedure is higher than that obtained via other laboratory-based methods, with theoretical maximum densities exceeding 10$^{18}$ per cubic centimeter. All of the pair production processes are well-known. Hence we can study this phenomenon using Monte Carlo simulations. Here we present simulation results using the CERN GEANT4 Monte Carlo code to model the experimental data obtained at the Titan (LLNL) laser. Once this code is successfully calibrated against existing data, we will use it to perform parameter studies, and design future targets to optimize the positron yield, density and e+/e- ratio.   

Thermalization and Cooling of Cold, Highly-Magnetized, One-Component Electron Plasmas

Thermalization of strongly-magnetized plasmas relies on the dynamics of particle collisions and interaction with the background electromagnetic field. The nature of these interactions changes greatly as a plasma is cooled to lower temperatures. In particular, these effects can have a large effect on techniques requiring sympathetic cooling through cyclotron radiation of a cloud of electrons. With the intention of cooling dense ($\sim 10^9 / \rm{cc}$) non-neutral plasmas to $4 \rm{K}$, we model the various mechanisms that are important in this regime. As a one-component plasma cools, the transverse and longitudinal degrees of motion become decoupled in collisions, inhibiting thermalization. Electromagnetic cavity modes couple in a complex manner to the electrons, changing the expected cyclotron radiation emission rates and absorption of energy from electrical noise. Here, we present a model for these mechanisms and a proposed experiment currently in construction for characterizing their behavior.   

Pressure and electrical resistivity measurements on hot expanded nickel: comparisons with quantum molecular dynamics simulations and average atom approaches

We present experimental results on pressure and resistivity on expanded nickel at low density (0.1\,g/cm$^3$) and high temperature (1-3\,eV). These data, corresponding to the warm dense matter (WDM) regime, are used to benchmark different theoretical approaches. A comparison is presented between fully 3-dimensional quantum molecular dynamics (QMD) methods, based on density functional theory, with average atom (AA) methods, that are essentially one dimensional. In this regime the evaluation of the thermodynamic properties as well as electrical properties is difficult due to the concurrence of density and thermal effects which directly drive the metal-non-metal transition. Experimental pressures and resistivities are given in a tabular form with temperatures deduced from QMD simulations.   

Thomas-Fermi model for Rydberg plasma clouds

We describe the effects of the electron trapping due to the background ions in ultra- cold plasmas, produced by excitation of Rydberg states in laser cooled atomic clouds. In the early stages of the ionization process, the ions are not thermalized with the electrons and can be described by a quasi-static Gaussian spatial profile, trapping the coldest fraction of the free electron population. In the present work, we study the electrostatic potential and the electron spatial profiles, in two different regimes. We show that in the strong confinement regime $\Phi\gg T/e$, a Rydberg plasma can be described by a Thomas-Fermi type of potential, similar to that obtained for heavy atomic species. The case of a non-neutral plasma cloud is also considered.   

Molecular dynamics simulation of ultracold neutral plasma

The ultracold neutral plasma is generated by photoionizing a ultracold gas, the typical electron and ion temperature are around $1\sim1000K$ and $1K$ respectively. The UNP pave the way towards an unexplored field of ultracold ionized gases and allow the discoveries of a series of new phenomena in atomic physics as well as in plasma physics. One of the motivations of studying ultracold plasmas is the fact that the ultracold plasma is a strongly coupled system. Disorder- induced heating (DIH) is one of the main reasons reducing the coupling strength in ultracold plasma. We demonstrate a numerical simulation for the dynamics of the ultracold plasmas using classical molecular dynamics method with open boundary. The simulation results of plasma expansion and DIH for different initial conditions are presented.   

Overview of Recent NSTX Research Facility Upgrades and Plans

The 2010 NSTX experimental campaign started with the Liquid Lithium Divertor (LLD) and the Beam Emission Spectroscopy (BES) commissioning. With lithium coating, ELM-free discharges were obtained over a wide range of lower triangularity and strike-point including on the LLD surface. Initial BES data was taken where coherent MHD activity was evident in spectrograms. For FY 2011, a second switching power amplifier for the non-axisymmetric coils, extra channels for the multi-pulse Thomson scattering, the MSE diagnostic based on laser-induced fluorescence, the tangential Fast Ion D-alpha and the tangential soft-x-ray diagnostics are being prepared. For a longer term NSTX facility upgrade, a new center-stack is being designed to double the toroidal field and plasma current while increasing the plasma pulse length from the present $\sim $ 1 s at 0.5 T to 5 s at 1 T. The second more tangential neutral beam is also planned to double the NBI heating power while improving NBI current drive efficiency. The upgrade will reduce the plasma collisionality toward those expected for the next step STs, and enable a demonstration of the fully non-inductive operation required for next-step applications.   

Overview of NSTX Liquid Lithium Divertor Performance and Divertor Upgrade Plans*

NSTX is investigating a Liquid Lithium Divertor (LLD) consisting of four plates forming an annulus 20 cm wide in the outer lower divertor. To contain the Li, the plasma facing surface of the plates was plasma-sprayed with a ~0.18 mm layer of semi-porous Mo. Reproducible, ELM-free, H-mode discharges were obtained with the OSP varied from well inside to directly on the LLD. All these exhibited higher energy confinement times, and reduced flux consumption early in the discharge relative to pre-lithium conditions. However, initially little pumping difference was apparent compared to solid Li coatings applied over the same region prior to installation of LLD. Planned upgrades include a fill system to transport liquid lithium directly to each LLD plate, and replacing the graphite plasma facing surfaces of the inner divertor with Mo. *Work supported by USDOE Contract DE- AC02-09CH11466.   

Characterization of Effect of LLD on Edge Plasma Parameters using High-Density Langmuir Probe Array

The NSTX Liquid Lithium Divertor (LLD) is designed to alter the edge plasma by providing a persistent particle sink with greater affinity than lithiated graphite surfaces for deuterium ions reaching the divertor target, thus lowering edge density while increasing edge temperature. In order to measure this effect, a 99-channel Langmuir probe array was designed and installed in an NSTX carbon divertor tile situated in the gap between two LLD plates. The Langmuir probes have the capability to measure the target electron temperature and density in either swept single-probe or continuous triple-probe mode. The probe array can also directly measure the incident ion flux from the plasma, which can be used to track the strike point location for applications in control system optimization and verification in conjunction with magnetic, $D_{\alpha}$, and IR camera data. In addition, offline and in-vessel RGA measurements of reactive lithium surfaces are analyzed using mass de-convolution to relate gaseous partial pressures to lithium activity, which is then correlated with $n_{e}$ and $T_{e}$ measurements from the probe array.   

Simulations of Diffusive Lithium Evaporation onto the NSTX Vessel Walls

The evaporation of lithium (Li) onto the NSTX divertor plates has reduced D recycling, improved confinement, and suppressed ELMs. However, in plasmas with suppressed ELMs, the core carbon and medium-$Z$ metallic impurity concentrations increase in the latter part of a discharge. To the extent that these impurities are the result of sputtering from the graphite tiles and other surfaces, increased coverage of the plasma facing surfaces with Li should reduce the impurity sources. This increased coverage can be achieved by evaporating the Li into a helium (He) filled vessel and exploiting the fact that the mean free path of the Li atoms scales inversely with the He pressure. Thus, higher (lower) pressures preferentially coat the top (bottom) of the vessel. A model for predicting and optimizing this process has been developed and validated against an initial set of deposition experiments. The model is found to agree with the data to within the estimated errors over a range of He pressures. The most significant uncertainties in the model have been identified and more discriminating validation tests are planned.   

Ultraviolet photoelectron spectroscopy analysis of lithium and deuterium interactions with graphite

Lithium wall conditioning has been implemented in fusion devices such as TFTR, CDX-U, FTU, T-11M, TJ-II and NSTX and has yielded improved plasma performance. Offline experiments at Purdue University have investigated the mechanism by which Li interacts with D. X-ray photoelectron spectroscopy (XPS) analysis has shown that deuterium irradiation induces interactions with Li-C and Li-O bonds. Ultraviolet photoelectron spectroscopy (UPS) shows Li$_{2}$O 2p orbital emission energy of 6.5 eV [1]. UPS probes the outermost valence electron orbital (probe depth $\sim $1nm), and yields information more sensitive to chemical bonding than XPS (probe depth $\sim $10nm). This work examines D interaction with lithiated graphite. Additionally, high-resolution electron energy loss spectroscopy (HR-EELS) provides complementary information regarding H bond hybridization.\\[4pt] [1] D. Ensling et al. Applied Surface Science 255 (2008) 2517--2523.   

Investigation of LLD Test Sample Performance Under High Heat Loads

A small prototype sample of the NSTX Liquid Lithium Divertor (LLD) was exposed to a MSE-LIF diagnostic neutral beam at a power of $\sim $10 MW/m$^{2}$ for 1-3 seconds. Calibrated infrared measurements of front face temperature and thermocouple measurements of bulk sample temperature were obtained. Predictions of temperature evolution were derived from a simple 1D heat flux model and compared with experimental data. These results demonstrated the effective heat load handling of a thin stainless steel liner with porous Mo coating on a copper heat sink, suggesting usefulness as NSTX-Upgrade PFCs. A novel method of measuring the resistance of the lithium films inside NSTX was also developed, the initial results of which will be presented.   

Triple Langmuir Probe Circuit Response to Dynamic Loading

Recently, an array of Langmuir probes was installed in the divertor region of the National Spherical Tokomak eXperiment (NSTX) and has been successfully tested [1]. The array is backed by a custom designed electronics system that allows biasing the probes, collecting the signals, reducing noise and amplifying circuitry and is suited to operate both as a single Langmuir probe and as a triple Langmuir probe (TLP). While the probe data has been useful in understanding the plasma characteristics during steady plasma discharges in NSTX, certain modifications aid interpretation of the transient events ($\sim \mu $s scale) such as during Edge Localized Modes (ELMs). During high-flux transients, the bias circuit may drift from the nominal values before on-board control circuitry can respond. The details of the circuit, its response to dynamic loading and the resulting impact on signal interpretation is presented. [1] M.A. Jaworski, J. Kallman, R. Kaita, H. Kugel, B. LeBlanc, R. Marsala, and D.N. Ruzic, ``Biasing, acquisition and interpretation of a dense Langmuir probe array in NSTX,'' 18th Topical Conference on High Temperature Plasma Diagnsotics, 2010.   

Lithium effects on the current profile in NSTX

Lithium coating of the plasma facing surfaces has been used extensively in NSTX, both on the carbon tiles and now on a Liquid Lithium Divertor. Improvements in electron confinement have been observed at mid-radii in the profiles for some lithiated plasma discharges. The effects of lithium on the current, q, and magnetic shear profiles are examined and correlated to these changes in transport and will be compared for discharges run with solid and liquid lithium on the dirvertor. The analyses of of NSTX plasma equilibria use data from the upgraded 18 channel Motional Stark Effect (MSE) diagnostic. Issues that should be considered in this analysis include changes in impurity profiles and pedestal characteristics. Supported by US DOE contracts DE-FG02-99ER54520 and DE-AC02-09CH11466.   

Edge profile and stability analysis as ELMs disappear with increasing lithium wall coatings in NSTX

Future tokamaks are not likely to be successful unless edge localized modes (ELMs) in high confinement plasmas can be eliminated or greatly reduced. Recently, lithium wall coatings in the National Spherical Torus Experiment have led to complete suppression of ELMs. Previous edge stability calculations indicated that ELMy pre-lithium discharges were unstable to low-n peeling or ballooning modes, while broader pressure profiles stabilized the ELM-free post-lithium discharges.\footnote{R. Maingi, et. al., Phys. Rev. Lett. 103, 075001 (2009)} This poster presents analysis of edge stability for the entire lithium coating thickness scan, i.e. intermediate cases in which lithium has reduced ELM frequency and generated small periods of ELM-free quiescence. In general the stability calculations show that the ideal growth rates are continually reduced as the lithium is increased.   

Can Injected Lithium Granules Trigger ELMs?

Coating plasma facing components (PFCs) with lithium has eliminated ELMs in NSTX H-mode plasmas. Improved ELM-free confinement, however, leads to accumulation of high-Z impurities and uncontrolled radiation losses. Further, injecting solid deuterium pellets in other devices is known to trigger ELMs at frequencies approximating the injection frequency. Hence, one can pose the question:''can lithium granules (i.e. small pellets) injected at high frequency also trigger ELMs in fusion devices?'' Such a scheme might lead to the replacement of large amplitude Type-1 ELMs with small amplitude, high frequency (grassy) ELMs. These smaller ELMs would then reduce the power flux to PFCs (as compared to large ELMs) while \textit{perhaps} simultaneously purging the core of accumulated impurities. Such a technology, moreover, would not require cryogenics. The physics of this concept will be explored.   

Characterization of the L-H Power Threshold on NSTX

The L-H power threshold in NSTX is 20 - 40{\%} larger for helium plasmas than comparable deuterium plasmas. This result was obtained using modest plasma current (0.6 MA) discharges where the auxiliary plasma heating and current drive was provided by HHFW (30 MHz) RF with 90 degree strap-to-strap phasing (k$_{\vert \vert }$ = 8 m$^{-1})$. This experiment will be repeated on NSTX using higher plasma current (0.8 MA) discharges that are heated using HHFW with 180 degree phasing (k$_{\vert \vert }$ = 14 m$^{-1})$ in order to reduce the uncertainties associated with calculating the heating power and to utilize the GPI diagnostic to characterize the SOL turbulence around the time of the L-H transition. Another planned experiment will build on the observation that the L-H power threshold decreases as the lower x-point radius is increased on NSTX. This result is consistent with XGC calculations that predict an enhancement in the radial electric field due to increased ion-orbit losses. This research is supported by the US DOE Fusion Energy Postdoctoral Research Program administered by ORISE under contract number DE-AC05-06OR23100 and by the US DOE contracts DE-AC02-09CH11466 and DE-AC05-00OR22725.   

Progress in the Development of Advanced Spherical Torus Plasmas in NSTX

Recent experiments in the National Spherical Torus Experiment have explored lithium conditioned, high-beta, high elongation plasmas over a range of q$_{95}$. Notable achievements include a very low surface voltage of 130 mV sustained through the current flat-top and an NSTX record plasma stored energy of 440 kJ. In the absence of MHD activity, the current profile can be modeled as the sum of inductive currents, neoclassical pressure-driven currents, and neutral beam driven current with classical collisional processes only. However, when core MHD is present, anomalous fast ion diffusivity is required to match the current profile. Overall, cases with 65-70{\%} of the current driven non-inductively are common at higher field and lower current. Thermal transport in these plasmas is comparable to that predicted by the standard ITER H-mode scaling, and shows stronger I$_{P}$ and weaker B$_{T}$ scaling than in NSTX experiments that did not benefit from lithium conditioning and such strong shaping. Many of these discharges exhibited very low internal inductance, leading to a reduced no-wall beta-limit and enhanced resistive wall instability. This work was funded by the U.S. DOE under contract DE-AC02-09CH11466.   

Overview of NSTX divertor and plasma-material interactions diagnosis and modeling

The National Spherical Torus Experiment (NSTX) has recently upgraded the divertor floor with the Liquid Lithium Divertor(LLD) and a dense Langmuir probe array. The array consists of electrodes operated as triple- and single-Langmuir probes. The improved diagnostic coverage enables characterization of steady and transient SOL characteristics as well as the use of the interpretative code, OEDGE (Onion-skin-method, EIRENE, DIVIMP edge). As prelude to OEDGE runs, a simple 2-point model OSM is applied to the Langmuir probe data to extract perpendicular transport properties in the SOL for comparison with turbulence properties. The status of the NSTX SOL plasma characterization (steady and transient) with the probes and modeling efforts are presented. Supporting experiments characterizing the LLD material will also be described along with the implications toward future modeling.   

Source and effects of turbulence and intermittent events in the scrape-off layer of NSTX

The gas puff imaging (GPI) diagnostic in NSTX is used to study the edge turbulence and intermittency present in the edge and scrape-off layer during H-mode discharges. Low power (and Ohmic) H-modes have quiescent edges with a low level of turbulence and intermittent blobs, while H-modes with strong auxiliary heating power exhibit intense edge activity. The turbulence and blob generation are studied in terms of global discharge parameters, edge profiles, and MHD activity. The possible contribution of enhanced cross-field transport due to the edge turbulence to the thermal scrape-off layer width is evaluated by comparing the outboard midplane GPI measurements with the heat deposition profiles on the divertor target plates measured by an IR imaging system. These results are also compared to ongoing modeling using the 2-D scrape-off layer turbulence code SOLT (Lodestar).   

Observations of Harmonic Oscillations and ELM Magnetic Precursors in NSTX

Recent experiments in the National Spherical Torus Experiment (NSTX) demonstrated the progressive suppression of edge localized modes (ELMs) with increasing lithium deposition. Sufficient lithium suppressed ELMs and made the occurrence of low-frequency, low-n harmonics more frequent. Signatures of these harmonic oscillations with a significant edge component were observed in both the high-n Mirnov magnetic and soft X-ray diagnostics of NSTX. Two distinct sets of harmonic oscillations can be observed during some ELM-free periods. The harmonic oscillations are consistent with modes localized in the edge with the frequency of the n = 1 harmonic near the rotation frequency of the edge plasma. NSTX magnetic diagnostics also observe distinctive signatures of ELMs. Transient n = 1 and n = 2 mode bursts and occasional higher n modes with frequency in the 30 to 90 kHz range occurred simultaneous with the increase in fast D$_{a}$ signal. These bursts of n = 1 and n = 2 modes resemble a model simulation of ELMs by T. Evans in which a bifurcation of magnetic topology is driven by nonlinear feedback amplification of thermoelectric currents from linear peeling-ballooning modes.   

Flow and Shear Behavior in the Edge and SOL in NSTX L-mode Plasmas

We describe the behavior of fluctuations in the edge and scrape-off layer (SOL) of NSTX L-mode plasmas, as observed by the gas puff imaging (GPI) diagnostic. Calculation of local, time resolved velocity maps using the HOP-V code enables analysis of turbulent flow and shear behavior. We observe periodic reversals in the direction of the poloidal flow near the separatrix. Also, we find that poloidal velocities and their radial shearing rate are well correlated with turbulent bursts indicated by an increase in $D_{\alpha}$ light in the SOL. The Reynolds shear stresses are found to exhibit significant negative skewness several centimeters inside the separatrix, which may be indicative of mean poloidal flow generation. Finally, a feature near 3 kHz is seen in the spectra of GPI intensity and poloidal velocity, which correlates with turbulent bursts. Furthermore, this mode exhibits some characteristics that are consistent with GAM-like behavior. Comparisons with SOLT turbulence simulations will be discussed.   

Response of Thermo-electrically Driven Scrape-Off-Layer Current (SOLC) during ELMs to Discharge Manipulation in NSTX Tokamak

The halo current diagnostic in NSTX shows that SOLC abruptly rises to robust amplitude during ELMs out of near-noise-level pre-ELM background with dynamic range up to 10$^2$ in far SOL, while undergoing temporal and spatial polarity reversals. An examination of response of SOLC to manipulation of the discharge may reveal possible connections of SOLC to ELM triggering and suppressing mechanisms. In preliminary studies to date, limited only to far SOL (R-R(strike pt) $>$ $\sim $ 40 cm), application of n=3 Resonant Magnetic Perturbations resulted in no readily discernible n=3-like structure in SOLC, and ramping up or down of the plasma current made no correlated changes in SOLC. Effect of lithium injection and biasing electrodes imbedded in divertor tiles to drive current will also be studied. Extension of these investigations into near SOL is planned.   

Comparison of Resistive Wall Mode Kinetic Stabilization Theory and Experiment

The theory of kinetic modification of ideal MHD stability has the potential to explain the physics of resistive wall mode (RWM) stability in high-beta tokamaks. The observation of unstable RWMs at plasma rotation frequencies between the stabilizing bounce and precession drift frequency resonances in NSTX is well explained by the kinetic theory$^{1}$, while energetic particles provide a stabilizing effect that is independent of plasma rotation. A description of the physics of RWM stability which may unify results between various devices is proposed. In certain cases large energetic particle stabilization may be preventing the RWM from going unstable except when triggered by a sudden loss of energetic particles. In NSTX, smaller energetic particle stabilization may be allowing the mode to go unstable more often, and for thermal resonances to be more clearly seen. This hypothesis is applied to analysis with the MISK code of plasmas from NSTX and other devices exhibiting RWMs with various levels of rotation and energetic particle content. [1] J. Berkery et al., \textit{Phys. Rev. Lett.} 104, 035003 (2010).   

High resolution MHD mode structure measurements via multichannel reflectometery in NSTX

MHD activity [e.g. Alfv\'{e}n eigenmodes (AE) and tearing modes] plays a critical role in many aspects of plasma performance. AEs, for instance, can significantly impact fast-ion transport in neutral beam heated plasmas. The investigation of MHD activity in NSTX has been aided by an array of fixed-frequency quadrature reflectometers used to determine the radial density perturbation structure of a variety of modes. Recently, the array was upgraded from 5 to 16 channels. The maximum frequency, which was 50 GHz, was also increased, so it now spans 30 -- 75 GHz ($n_{cutoff}$ = 1.1 -- 7.0 x 10$^{19}$ m$^{-3}$ in O-mode). The upgrade improves radial resolution in structure measurements, while also allowing access to higher density plasmas, including, in particular, H-mode plasmas. Structure measurements highlighting these capabilities are illustrated for a variety of MHD modes, including tearing modes, energetic particle modes and internal kinks (f$\sim $1~--~25 kHz), reverse shear and toroidicity-induced AEs (f$\sim $50 --~200 kHz) and compressional and global AEs (f$\sim $0.5 --~2.5 MHz).   

Multi-mode RWM analysis of NSTX high beta plasmas

The behavior of resistive wall modes (RWM) in the NSTX device has been examined with the multi-mode VALEN computer code. Experiments at very high-normalized beta reaching 7.4 in conditions with the ideal MHD no-wall limit near 4 were produced in NSTX and are analyzed to compare the multi-mode model with experiment. Multi-mode VALEN includes conducting structures, coils, and plasma response as an L-R circuit [1]. We summarize the multi-mode formulation and contrast it with single-mode VALEN [2]. We present multi-mode characteristics of RWM behavior for NSTX high beta plasmas including the mode-spectrum evolution for passive growth and the interaction of the mode spectrum with exterior fields. The response to applied fields is studied in the time domain as well as via frequency response. \\[4pt] [1] A.H. Boozer, Phys. Plasmas 10 (2003) 1458 \\[0pt] [2] J.M. Bialek et al. Phys. Plasmas 8 (2001) 2170   

Measurements and modeling of prompt loss of neutral beam ions from NSTX

Prompt loss of neutral beam ions in tokamaks can occur when the injected neutrals are ionized such that their orbits intersect solid objects near the plasma. Such losses are typically large at low plasma current, but diminish rapidly with increasing current. NSTX is equipped with a scintillator fast ion loss diagnostic that can detect prompt losses. Since other plasma phenomena, such as MHD activity, can also induce beam ion loss, it is useful to have a model that can predict the range of pitch angles that will experience prompt loss to the detector in a given plasma configuration. This then permits identification of which losses are prompt and which arise from other causes. A velocity space based prompt loss model has been developed for NSTX that predicts pitch angle distributions similar to those measured in NSTX plasmas. The model offers some possibility for extension to other fast ion diagnostics and to other loss mechanisms.   

Effects of toroidal rotation shear on TAE dynamics in NSTX

The effects of a sheared toroidal rotation on the dynamics of bursting toroidicity-induced Alfv\'{e}n eigenmodes (TAEs) are investigated experimentally in neutral beam heated plasmas on the National Spherical Torus Experiment. The modes extend over most of the minor radius across a region where a strong toroidal rotation shear of up to 200 kHz/m is measured. Contrary to results from other devices, no clear evidence of increased damping is found. Instead, experiments indicate a strong correlation between the TAE dynamics and the instability drive. For instance, the amplitude of the bursts increases as the fast ion population builds up and otherwise stable TAEs can be promptly destabilized by auxiliary rf heating, due to modifications of the fast ion distribution. It is argued that kinetic effects involving changes in the mode drive and damping mechanisms other than rotation shear, such as continuum damping, are mostly responsible for the bursting dynamics of the modes.   

Transient Enhancement (`Spike-on-Tail') Observed on NBI Energetic Ion Spectra Using the E$\vert \vert $B NPA on NSTX

An $\sim $ 4x increase in the E$\vert \vert $B Neutral Particle Analyzer (NPA) charge exchange neutral flux localized at the Neutral Beam Injection (NBI) full energy is observed in the National Spherical Torus Experiment (NSTX). Termed the High-Energy Feature (HEF), it appears only at the NBI full energy, exhibits a growth time of $\sim $ 20 - 80 ms, seldom develops a slowing down distribution and arises only in discharges where kink-type modes (f $<$ 10 kHz) are absent, TAE activity (f $\sim $ 10-150 kHz) is weak and CAE/GAE activity (f $\sim $ 400-1200 kHz) is robust. The HEF is observed only in H-mode discharges with P$_{b} \quad \ge $ 3 MW and v$_{\vert \vert }$/v $\sim $ 0.7 -- 0.9; i.e. only for passing ions. The HEF is suppressed by vessel conditioning using lithium deposition at $\ge $ 100 mg/shot. Coincident increases of $\sim $ 10-30 {\%} in neutron yield and total stored energy during the HEF are driven by plasma profile changes and not the HEF itself. Tentatively, the HEF appears to be caused by a form of CAE/GAE wave-particle resonant interaction.   

Characterization of fast ion confinement in the NSTX based on FIDA diagnostic measurements

Confinement of energetic ions is a critical issue for fusion devices. In last years, much interest has been devoted to losses or redistribution, in real and velocity space, caused by Alfv\'enic modes. More recently it emerged that, in absence of energetic particles modes, fast ions transport can differ from what expected from classical predictions. This work addresses experimentally the confinement of fast ions in NSTX. The radial fast ion density profile $n_f$, measured by the Fast Ion D$_\alpha$ (FIDA) diagnostic from the high energy tails of D$_\alpha$ emission, is characterized over an extended database of plasma discharges including L-mode, H-mode, and with different types of MHD and Alfv\'enic modes. Radial gradient of $n_f$, the drive of energetic particle instabilities, is observed to vary substantially in different plasma conditions. Dependence of $n_f$ peaking on plasma parameters (e.g. $I_p$, $n_e$, $B_t$) will be reported and compared with predictions based on classical fast ion transport.   

Improvements to a Fast-ion D$_\alpha$ Simulation Code

FIDASIM is a code that models fast-ion D$_\alpha$ (FIDA) light that is produced by charge-exchange reactions between fast ions and injected neutral beams in tokamak plasmas. Reactions with both the primary injected neutrals and with the cloud of secondary ``halo'' neutrals that surround the beam are treated. Accurate calculation of the fraction of neutrals that occupy excited atomic states (the collisional-radiative transition equations) is an important element of the code. Judicious selection of grid size and other parameters facilitate efficient solutions. D$_\alpha$ light from beam emission, direct charge-exchange with protons, and the beam halo are also calculated. For greater speed, conversions to FORTRAN and GPU are underway. FIDASIM has been applied to data from DIII-D, NSTX, ASDEX Upgrade, and MAST.   

Gyrokinetic analysis of thermal transport scaling in NSTX and MAST

It remains unclear how thermal energy confinement will scale when extrapolating from present-day STs to CTF conditions at higher plasma current and toroidal field (lower collisionality). To address this theoretically we present linear gyrokinetic simulations investigating microstability in the outer half-radius of NSTX and MAST discharges that vary I$_{p}$ and B$_{T}$. In high collisionality discharges (low I$_{p}$ {\&} B$_{T})$ microtearing modes are often predicted to be unstable. These modes are weakened when artificially reducing electron collisionality, consistent with experimental scaling trends at higher I$_{p}$ {\&} B$_{T}$. Whether other modes (ITG/TEM, ETG) arise depends on additional parameters such as profile gradients, effective ionic charge, beta, and flux surface shaping. We also discuss the numerical complications in non-linear microtearing mode simulations that include electromagnetic perturbations, collisions and toroidal flow and flow shear. This work is supported by US DOE contract DE-AC02-09CH11466.   

Nonlinear Gyrokinetic Turbulence Simulations of the NSTX Spherical Torus

The National Spherical Torus Experiment provides a unique environment for the study of electron turbulence and transport. We present nonlinear GYRO\footnote{J. Candy and R. E. Waltz, J. Comput. Phys. {\bf 186}, 545 (2003).} simulations of microturbulence in NSTX discharges and make comparisons between numerically simulated and experimentally measured levels of electron-scale turbulence. In particular we examine the effects of magnetic shear, ${\mathbf E\times B}$ shearing and collisionality on turbulence driven by the Electron Temperature Gradient (ETG) mode, while paying attention to the roles of electromagnetic fluctuations, kinetic ions and realistic experimental NSTX parameters. We also investigate the interplay between electron turbulence and transport using the TGYRO\footnote{J. Candy et al., Phys. Plasmas \textbf{16}, 060704 (2009).} simulation suite. This work is supported by the SciDAC Center for the Study of Plasma Microturbulence, DOE Contract DE-AC02-09CH11466, and used the resources of the National Center for Computational Sciences at ORNL, under DOE Contract DE-AC05-00OR22725.   

Study of High-k Turbulence with Microwave Scattering on NSTX

A comprehensive understanding of plasma turbulence and its relation to electron transport requires measurements of both large and small wavenumbers. Due to its low toroidal field and low aspect ratio, the National Spherical Torus eXperiment (NSTX) provides a unique laboratory to study the short- wavelength, electron-scale turbulence and its relation to electron transport. The electron-scale turbulence is studied on NSTX using a microwave scattering diagnostic capable of measuring the turbulence spectrum as a function of radial wavenumber with high spatial localization. Recent improvements in the scattering configuration and an upgraded microwave source allow the simultaneous measurement of more wavenumbers than were measured before, which makes more detailed comparisons with gyrokinetic simulations possible. We will discuss k spectra measured in both L and H-mode plasmas, as well as parametric dependence of high-k turbulence in H-mode plasmas. Comparison with non-linear gyro-kinetic simulations will be presented. Work supported by US DOE Contracts DE-AC02- 09CH11466 and DE-FG02-99ER54518.   

Validation of nonlinear ETG simulations against measurement of short-scale turbulence on NSTX

The comparison between density fluctuations measured with coherent scattering techniques and spectra from space resolved fluctuations computed from nonlinear gyro-kinetic codes are affected by a number of systematic errors and uncertainties. These include the scattering localization, the different wavenumber range covered, the simulation runtime, which mainly affect the slope of the k-spectrum. To bridge the gap between experiments and simulations, a synthetic diagnostic has been developed. Taking into account the beam propagation, the beam intensity profile at the location of scattering and the instrument transfer function, the synthetic high-k predicts the collection efficiency in the ($k_r,k_\theta$) space. When simulated spectra are filtered by the synthetic high-k, a closer agreement with experiments is found. Results from nonlinear simulations run in different plasma configurations, including L-mode and H-mode, will be presented.   

Reflectometry and Backscattering for Broad-$k_r$ Microturbulence Measurements in NSTX

On NSTX, the unique combination of reflectometry hardware (FM-CW, fixed-frequency, and correlation reflectometers) is well-suited to turbulence measurements. Recently, the FM-CW reflectometers have been used as radial backscattering diagnostics for probing microturbulence over a broad range of radial wavenumbers ($k_r$$\sim$0$-$20 cm$^{-1}$). This new method utilizes the reflection from the cutoff layer to determine a detailed reconstruction of the density profile. Time-of-flight information is then used to map the backscattered signal to radial locations away from the cutoff layer, allowing visualization of the turbulence intensity in $k_r$ vs $R$ (major radius) space with excellent space and time resolution. Further details of the method are demonstrated using modeled turbulence and the GPU-accelerated UCLA 1-D and 2-D FDTD full-wave codes. Initial measurements during the L-H transition show a steep drop in the turbulence intensity over a broad range of $k_r$ and localized to a narrow spatial region around the edge transport barrier location.   

The NSTX BES System for Measuring Small-Scale Density Fluctuations

A new Beam Emission Spectroscopy (BES) diagnostic has been deployed at the NSTX. It exploits new detectors and optical systems adapted to the large pitch angles on the spherical torus. The detectors consist of surface-mount, wide-area photoconductive photodiodes and a new frequency-compensated broadband preamplifier to achieve photon-noise limited measurements. Advantages of the new system include an increased effective bandwidth of 1 MHz and elimination of the need for cryogenic cooling. First measurements have been obtained using 16 channels, with plans to expand to 32 in the near future. These measurements show coherent and broadband plasma turbulence in high gradient regions, and coherent modes that mainly correlate with Alfv\'{e}n/energetic particle modes. To support these BES experiments at NSTX and similar ones at DIII-D, Langmuir probe measurements in \textsc{Pegasus} ST plasmas are being evaluated for validation of velocimetry techniques using 2D BES \~{n} measurements.   

Poloidal flux from Coaxial Helicity Injection in NSTX

Transient coaxial helicity injection (CHI) has been employed on the National Spherical Torus Experiment (NSTX) to produce plasmas that can be ramped-up in current by induction. A capacitor bank of up to 50 mF charged up to 1.75 kV is connected across the electrically isolated inner and outer vacuum vessel segments by an ignitron switch. As the injector current (I$_{inj})$ linking the inner and outer divertors increases, the J$_{pol} \quad \times $ B$_{T}$ force overcomes the field line tension and the plasma expands until it fills the torus volume. After a pre-programmed time (typically 2.5 to 5 ms) near the peak in the toroidal current, the capacitor bank is diverted into a low resistance by a second ignitron. The plasma detaches from the electrodes to form closed flux surfaces. CHI discharges with up to 0.3 MA of toroidal plasma current have been ramped up inductively to reach higher final current with higher poloidal flux than purely inductive discharges with the same applied flux.   

Resistive MHD modeling of Coaxial Helicity Injection (CHI) in NSTX

CHI has generated plasma with current, density, and temperature appropriate for NSTX startup [1] offering the potential of solenoid-free operation of an advanced ST. Whole-device simulations using the NIMROD MHD code [2] have been initiated to extend physics understanding of CHI in NSTX and other STs and to help guide experiments. A computational grid has been developed and boundary conditions applied for external magnetic fields including eddy currents in walls and stabilizing plates. Injection and absorber slots are modeled with current specified at the injector and ExB drift at the absorber to prevent compression of the vacuum toroidal magnetic field, as done in simulations on HIT-II. [3] Initial results will be presented and compared with experiment. Results will also be compared with simulations of the SSPX spheromak [4] to examine the different behaviors in the (q$>$1) ST and (q$<$1) spheromak. 1. R. Raman, et al., Phys. Rev. Letters \textbf{104}, 095003 (2010). 2. C.R. Sovinec, et al., J. Comp. Phys \textbf{195}, 355 (2004). 3. A. Bayless, C.R. Sovinec, unpublished. 4. E. B. Hooper, et al., Phys. Plasmas \textbf{15}, 032502 (2008).   

High Power Operation of the Upgraded NSTX HHFW Antenna Array

The single-feed, end-grounded straps of the NSTX 12-strap HHFW antenna array have been replaced with double-feed, center-grounded straps while keeping the remaining antenna geometry unchanged. The peak voltages and electric fields in the vicinity of the Faraday shield have been halved for the same strap currents, permitting a direct examination of the roles that strap voltages and currents play in determining antenna power limits in the presence of plasmas. Plasma operation cleaned enough Li deposits, accumulated during prior wall conditioning, from the antenna surfaces to reach coupled powers in excess of 4 MW in L-mode plasmas in 2009. The center-grounded straps were less susceptible to arcing during ELMing H-mode plasmas than the end-grounded straps had been. A fast framing, visible light camera monitors the full antenna array; an arc can usually be associated with expulsion of Li from the FS/antenna frame surfaces in its immediate vicinity. The voltage holding and power levels obtained during the 2010 campaign will be reported and the limiting mechanisms will be discussed.   

HHFW Heating Properties for H-mode Plasmas in NSTX

High harmonic fast wave (HHFW) heating properties for ELM-free and ELMy H-mode plasmas are being compared to investigate the effects of ELMs on HHFW heating efficiency and edge HHFW power losses. In general, core heating is reduced and edge heating is increased in the NB and HHFW driven ELMy H-mode regimes. The goal is to determine to what extent the reduction of core heating with ELMs is due to an increase in electron stored energy loss versus a relative increase in the edge HHFW power that is deposited in the edge/divertor region. Measurements of core heating effects (Thomson scattering, magnetics - EFIT, etc.) and of the divertor RF heating/interactions (IR cameras, RF probes, Langmuir probes, etc.) will be presented for a number of cases to elucidate these RF power loss effects. Fast IR data indicate that the bulk of the ELM ejected energy from the core plasma is deposited in the vicinity of the outer strike radius, falling off rapidly toward the radial zone of the edge RF power deposition in the divertor. Direct observation of the divertor edge RF deposition zone with the fast IR camera is planned to quantify the effect of the ELMs there. Work supported by USDOE Contract No. DE-AC02-09CH11466.   

High Resolution Full Wave Modeling of Fast Waves in NSTX

High Harmonic Fast Waves (HHFW) are being used in NSTX for plasma heating and noninductive current profile control. Numerical solutions for the wave fields obtained with the full wave TORIC and AORSA codes with ultrafine spatial resolution reveal the presence of a short wavelength feature that is predominantly polarized in the direction parallel to the equilibrium magnetic field and which is predicted by the codes to damp on electrons. A similar short wavelength mode also appears in simulations of the rf fields in C-Mod in the ICRF regime. Preliminary analysis indicates that the mode may be related to a slow mode that can propagate above the fundamental ion cyclotron frequency. The predicted power deposition profiles will be compared to those inferred from experimental measurements to see if the mode has a significant effect on the wave propagation and absorption. Possibilities for detecting the mode in NSTX and C-Mod will be discussed.   

HHFW power absorption in NBI target plasmas

Experimental and analytic work is ongoing to ascertain the efficiency of using high-harmonic fast waves (HHFW) to inject auxiliary power into NBI heated NSTX plasmas. As a result of progress in understanding edge effects relevant for wave coupling, HHFW power is routinely deposited within the last closed flux surface . Increases of the plasma stored energy, the electron temperature and the neutron production rate are observed when HHFW power is applied. Two mechanisms compete for the absorption of the HHFW reaching the main plasma: (1) electron heating via Landau damping and transit-time magnetic pumping; (2) rf acceleration of NBI generated fast ions. The power absorption will be investigated by comparing the experimental data with analyses and predictions from the TRANSP/TORIC, GENRAY and CQL3D codes. This work is supported by DOE contract DE-AC02-09CH11466.   

Key Aspects of EBW Heating and Current Drive in Tokamaks

Electron Bernstein wave (EBW) heating and current drive is modeled by coupled mode conversion, ray-tracing (AMR) and Fokker-Planck (LUKE) codes. Deposition and current drive profiles are determined for EBW with various injection parameters under realistic spherical tokamak conditions. There parameters are varied to investigate the robustness of the applied scenarios. The importance of relativistic corrections to EBW absorption is considered. The differences between various relativistic models are explored.   

Multivariable Model-based Shape Control for the National Spherical Torus Experiment (NSTX)

Because of the coupling between the different geometrical parameters, multi-input-multi-output (MIMO) model-based shape controllers are necessary to achieve the very stringent plasma shape requirements in highly-efficient tokamaks. Leveraging the availability of rtEFIT, we propose a robust model-based MIMO controller to provide real-time shaping and position control of the plasma in NSTX. The proposed controller is composed of three loops that transform the shape control problem into a tracking problem. A singular value decomposition of the plasma model is carried out to define the weights associated to the tracking errors. The $H_{\infty }$ technique is used to minimize the tracking errors and optimize input efforts. Computer simulation results illustrate the performance of the robust shape controller, showing the potential for improving the performance of present non-model-based controllers.   

Conceptual design of real-time density control via FIReTIP in NSTX

Real-time density feedback control is desirable in tokamaks to avoid low-density discharges and for scaling experiments. The NSTX density feedback control system has been designed in conjunction with the Far Infrared Tangential Interferometer/Polarimeter (FIReTIP). FIReTIP signals are sampled at 5 kHz, using a plasma control system (PCS) for real-time correction of fringe jump errors. Raw data obtained from 2010 experiments have been analyzed with a new PCS algorithm comprised of status indicator, density convertor, fringe jump corrector and feedback controller. Converted density signals from measured data are compared to reference data and converted to gas flow rates through existing PCS gas-injector-system categories. The hardware and software configuration of the feedback control system and experimental test results will be presented with a discussion of control algorithms for density evolution.   

Modeling and laboratory test of a prototype polarimeter for magnetic fluctuation measurements on NSTX

Polarimetry is a powerful technique capable of probing magnetic field fluctuations in fusion plasmas. [W. X. Ding et al. Phys. Rev. Lett. \textbf{90}, 035002 (2003).]~A 288 GHz polarimeter operating along a major radial chord in a retroreflection geometry is being developed for NSTX to determine magnetic fluctuations in the frequency range from 1$\sim $100 kHz. Modeling is used to investigate the sensitivity of this planned system to magnetic fluctuations resulting from tearing modes, Alfv\'{e}n eigenmodes, etc. Preliminary analysis suggests that measurement of relative magnetic fluctuation levels $\ge $ 0.1{\%} is feasible. Previous calculations based on NSTX plasma equilibria have revealed an interaction between Faraday rotation and Cotton-Mouton effects, which can complicate interpretation. [J. Zhang et al. RSI (Oct, 2010).] A prototype system is under laboratory test to determine measurement sensitivity and establish the optimum detector configuration for measurement of the full polarization state.   

Installation of the MSE-LIF Diagnostic on NSTX

The motional Stark effect with laser-induced fluorescence diagnostic (MSE-LIF) is presently being installed on NSTX for demonstration in the 2011 run year. The MSE-LIF will enable radially resolved measurements of the magnetic field pitch angle and magnitude, both of which can be used to constrain plasma equilibrium reconstructions. A diagnostic neutral beam with low axial energy spread, low divergence, and high reliability has been developed. It operates routinely at 35 kV and 40 mA. A laser has been developed with high power ($\sim $10 W) and optimal linewidth match to the neutral beam ($\sim $6 GHz). The laser wavelength is near 651 nm for a match to the Doppler-shifted Balmer-alpha transition in the beam neutrals. The unique high-power, moderate linewidth laser system utilizes a 19 emitter diode laser bar and feedback from a volume holographic grating. A magnetic shield protects the ion source from the NSTX stray fields. This poster will present the final system design and give predictions for performance on NSTX.   

New opportunities of physics study by FIReTIP and Poloidal Scattering system on NSTX-Upgrade

A reconfiguration of the Far Infrared Tangential Interferometer/Polarimeter (FIReTIP) and the high-k scattering systems are planned for the National Spherical Torus Experiment (NSTX) Upgrade (FY2013-14). The FIReTIP upgrade design comprises three channels: a core channel (R$_{T} \sim $ 40 cm) for the main density monitoring and real time density feedback control, a middle channel (R$_{T }\sim $ 90 cm) for HHFW heating localization studies and MHD studies including Alfven Eigen modes, and an edge channel (R$_{T} \sim $ 140 cm) for the boundary electron density fluctuation measurements which are important for H-mode and pedestal physics studies. The high-k scattering system will be reconfigured as a poloidal scattering system for measurement of k-spectra relevant to ETG modes. Details of the reconfiguration plan will be presented with recent physics results, together with a discussion of the physics areas to be addressed with the upgraded diagnostic tools.   

Application of fast dual-band infrared on NSTX

The ORNL fast infrared (IR) camera on the National Spherical Tokamak Experiment (NSTX) device has been upgraded to simultaneously observe dual IR bands at its maximum frame rate, 1.6 kHz, in order to nearly eliminate dependence of the measured emission on surface emissivity. An image splitter was developed to project both IR channels -- the 4-6 micron medium wavelength, and the 7-10 micron long wavelength bands -- side by side on the broadband HgCdTe detector in the camera; the splitter has been upgraded to include the use of hybrid diffusive optical element (DOE) lenses in order to reduce chromatic aberration and to improve image quality and dynamic range. Using this instrument, the relationship between the emission ratio and surface temperature for a variety of camera parameters, and the impact on the resulting heat flux profile calculated from IR video are investigated.   

Large area divertor temperature measurements using a high-speed, near-infrared camera in NSTX

IR band-pass filters ($>720$ nm or $> 900$ nm) were used with a Phantom 7.3 high-speed camera to try to measure the surface temperature of plasma facing components and the Liquid Lithium Divertor (LLD) in NSTX. The present camera looks through an upper port with a view of more than half of the lower divertor. With several megawatts of RF heating power, the observed surface temperature increased by $\sim$700 $^{\circ}$C in a localized region magnetically connected to the RF antenna. Such a wide-angle, high-speed (up to 10$^4$ fps) IR system could also evaluate the thermal response to transient events such as ELMs and disruptions, which can cause large, uneven heat loads over a wide area of the divertor. The rise/fall time during power transients and emission spectroscopy diagnostics were used to help distinguish plasma IR line emission from surface blackbody emission. The entire system has been calibrated with a blackbody source from 350 to 700 $^{\circ}$C.   

Results of mobile dust studies in NSTX

Operational and safety concerns over the amount of intrinsic dust that will be generated in next-step tokamaks has initiated many avenues of dust studies. Mobile dust studies have been performed on NSTX by dropping pre-characterized Li and tungsten dust with mean diameter of 44$\mu $m and 10$\mu $m, correspondingly, into the upper regions of the scrap-off layer. Two fast visible cameras separated spatially but viewing the same plasma region have been utilized to create 3-D trajectories of the dust tracks. It has been found that the Li and W particles are accelerated by the flows in the peripheral plasma, while the tungsten particles appear to penetrate deeper to the SOL before ablating away. The Li results have been used for validation of the DUSTT/UEDGE code and good agreement between measured and simulated trajectories was obtained. It was found that the amount of Li introduced can have a significant impact on the edge parameters. The Li and W trajectories will be presented and the impact of the dust on the plasma edge will be discussed.   

Multi-energy Soft X-ray diagnostic for NSTX

A high resolution, ``multi-energy'' soft X-ray (ME-SXR) diagnostic is being developed for the NSTX edge plasma. The system will measure with spatial resolution of $\le $1cm and with $\sim $10 kHz bandwidth the XUV and SXR emission from the outer NSTX regions, including the pedestal, and will serve for studies of edge particle and electron transport, of ELM dynamics, and other edge phenomena. The system comprises five tangential AXUV diode arrays, viewing the plasma between 0.5$<$r/a$<$1.1 through filters of varying composition and thicknesses, including a bare diode array. The filters provide a coarse sub-sampling of the XUV-SXR spectrum and will enable measuring changes in the electron temperature, density, and impurity concentration, on fast time scales. The obtain the electron temperature and the particle density the emissivity profiles are modeled using a coronal atomic model and a look-up table algorithm. In addition, a Transmission Grating imaging spectrometer is used to constrain the impurity fractions in this model.   

Modeling impurity distribution in an ST tokamak using a transmission grating based diagnostic in the EUV range

A free standing transmission grating based imaging spectrometer is used to monitor impurity radiation emitted by the NSTX tokamak in the EUV range covering $30-700$ {\AA} (D. Kumar et. al., Rev. Sci. Instrum., in print). The spectrometer can successfully distinguish between the space distribution of the charge exchange radiation of C, O and N ions (localized to the beam interaction region), the edge emission from low Z elements and the core emission from high Z impurities, such as Cl. However, because of the mid plane toroidal view of plasma the spatial profiles of various lines are hard to interpret quantitatively. A geometric model based on the atomic data provided by ADAS is being developed to estimate the impurity spatial distribution. The spectrometer operates at a time resolution of $\sim 400$ ms. An upgrade to a faster detection system is presently implemented and the corresponding results will also be shown.   

The Material Analysis Particle Probe (MAPP) as an in-situ plasma-material interaction diagnostic in NSTX

The National Spherical Torus Experiment uses lithium as a plasma-facing surface to enhance plasma performance. Control of hydrogen recycling is dependent on surface chemistry of lithium depositions on graphite and metallic substrates. To characterize the surface chemistry evolution of the in-vessel surface during plasma irradiation a new Material Analysis Particle Probe (MAPP) has been designed that exposes in-situ samples to dedicated NSTX plasma shots. After exposure the samples are retracted in-vacuo to an analysis chamber and examined by a suite of surface analysis tools such as: XPS, LEISS and TDS. The data interpretation is aided by lab experiments that measure the properties of lithiated graphite and lithium coatings on porous Mo surfaces (i.e. in the liquid lithium divertor) identical to those used in NSTX. Results from MAPP design and testing as well as lab experiments on D- irradiated lithium-based surfaces will be presented.   

RAPTOR: Optimization, real-time simulation and control of the tokamak q profile evolution using a simplified transport model

Control of the plasma current density and safety factor profile evolution in a tokamak is crucial for accessing advanced regimes. The evolution of the current density profile is steered by a combination of inductive voltage and auxiliary current drive actuators, and is nonlinearly coupled to the evolution of the (ion/electron) temperature and density profiles. Using appropriate simplifications, a model has been obtained which can be simulated on time scales faster than the tokamak discharge itself, but still retains the essential physics describing the nonlinear coupling between the profiles. This model, dubbed RAPTOR (Rapid Plasma Transport simulatOR) has been implemented in the new real-time control system on the TCV tokamak at CRPP, and can be used for real-time reconstruction and model-based control of the q profile. It can also be used off-line to determine optimal actuator trajectories in open loop simulations to steer the plasma profiles towards their required steady-state shapes while remaining within a constrained set of allowable profiles.   

BSC{\_}T: A Tool For Efficient Magnetic Field Computation

The modeling of fusion plasmas requires the accurate modeling of the fields which confine these plasmas. BSC{\_}T is a Fortran module which allows for accurate and expedient computation of these fields from the currents which produce them. Near field producing elements, analytic solutions are used to retain maximum accuracy for geometries such as pure dipoles, infinite line currents, current rings, and finite current segments [1]. At greater distances, series expansions are used to quicken calculation with little loss of precision. More complex geometries may be modeled by arrays of these simple geometries and by current carrying mesh forms. Accuracy and performance benchmarks are presented, as well as reconstructions using the V3FIT code with various vacuum vessel models.\\[4pt] [1] J. D. Hanson and S. P. Hirshman, Phys. Plasmas \textbf{9}, 4410 (2002).   

Status of TRANSP

This poster describes the status of TRANSP code development and run production operations. Production rates continue to climb as new users are added; statistics will be shown, including utilization of the recently added TRANSP MPI capability. Code configuration for between shots analysis is now possible, and is being used in the NSTX control room. There have been significant developments in free boundary modeling capability (Isolver), RF component physics options (GENRAY, CQL3D, and TORIC), and fast ion modeling (NUBEAM); summarized here, separate posters will cover the NUBEAM and RF component improvements in detail. Status of TRANSP predictive modeling capabilities and development efforts (PTRANSP) will be described. A new method for making use of TRANSP output archives, via Swim SciDAC Plasma State files, will be presented.   

Status of new RF heating and current drive capabilities in TRANSP

This poster describes our recent efforts to incorporate new RF heating and current drive capabilities into the tokamak transport code TRANSP. Efforts are underway on two fronts: (1) incorporate new RF heating/current drive modules and (2) improve the performance of existing RF codes by utilizing the parallel processing capabilities of the codes. On the first front, we have made progress by incorporating the generalized ray tracing code GENRAY into TRANSP and making it available for ECRH calculations. We are also making progress on incorporating the bounce averaged Fokker-Planck code CQL3D into TRANSP. On the second front, we have demonstrated significant speedup of a TORIC calculation when the new 2D parallelized TORIC is used on the PPPL Kruskal cluster. We are currently carrying out a demonstration of the speedup of a complete TRANSP run with parallelized toric.   

Validation of improved Multi-Mode model for density, temperature and toroidal rotation profiles using PTRANSP simulations

Advances in the Multi-Mode model include an improved Weiland model for the ITG and TEM modes [1] and a new model for the drift resistive inertial ballooning modes (DRIBM) [2]. Advances in the PTRANSP code include an improved algorithm for the particle density evolution. Validation studies are carried out for the improved Multi-Mode model using PTRANSP simulations. In order to allow tight coupling with stiff transport models, all of the transport equations for main ion and impurity density profiles as well as electron temperature, ion temperature and toroidal angular rotation profiles are advanced simultaneously by the PTRANSP solver. The Plasma State connects the new solver to the rest of PTRANSP. The solver uses several techniques to control numerical stability. Simulation results for density, temperature and rotation frequency profiles are compared with experimental data for L-mode and H-mode discharges. \\[4pt] [1] J.Weiland et al., Nucl. Fusion 49 (2009) 965933; F.D. Halpern et al., Phys. Plasmas 15 (2008) 065033 \newline [2] T. Rafiq et al., to appear in Phys. Plasmas (2010)   

Spectral Basis Functions for Ideal and Extended MHD

The ability to reliably reproduce and distinguish various modes of ideal and extended MHD in numerical computation depends sensitively on the choice of spatial representation. The original development of ideal-MHD eigenvalue solvers [Gruber and Rappaz, Springer-Verlag (1985), for example] provides a numerical foundation. However, the interactions of transport with magnetic topology evolution in nonlinear simulations impose additional criteria that favor high-order and spectral representations. We compare global spectral representations and spectral-element representations for several possible systems of variables in ideal and non-ideal cylindrical eigenvalue computations. While many of the conclusions from the original low-order eigenvalue computations hold for second-order systems for displacement, first-order systems for all physical components are more representative of time- dependent computations and have distinct numerical properties. As expected, global representations converge slowly for localized modes, but placing borders of spectral elements at rational surfaces leads to rapid convergence.   

NIMROD Simulations of FRC Formation and Merging

When FRCs are formed and translated in a conical $\theta $-pinch or by sequencing the coils, a toroidal field is spontaneously generated. This is thought to be due to the action of the Hall term during the reversal process, but previous modeling did not fully explain it [1]. Preliminary studies with NIMROD show that inclusion of the Hall term leads to the generation of both toroidal fields and flows. This will be investigated further with improvements to the radial boundary conditions, and a more detailed study of this phenomenon will be discussed. In addition, a numerical study of the translation and merging of two $\theta $-pinch formed FRCs has begun. Preliminary calculations show that inclusion of the Hall term can have a significant effect on the merging process. Three-dimensional effects have not been a part of past simulations of $\theta $-pinch FRC formation and translation, but will form an important part of this study.\\[4pt] [1] Richard D. Milroy and J.U. Brackbill, ``Toroidal magnetic field generation during compact toroid formation in a field-reversed theta pinch and conical theta pinch'', Phys. Fluids \textbf{29}, 1184 (1986)   

Hybrid Kinetic-MHD Studies of FRC's using Lorentz $\delta\!f$ PIC in Finite Elements

We report progress on the extension of the drift kinetic $\delta\!f$ Particle-in-Cell (PIC) module\footnote{C. C. Kim ``Impact of velocity space distribution on hybrid kinetic-magnetohydrodynamic simulation of the (1,1) mode'', Phys. Plasmas 15, 072507 (2008)} to a Lorentz force model for the NIMROD code. Resolution, both temporal and spatial, of the full Lorentz orbit is necessary to capture the energetic ion physics in Field Reversed Configurations (FRC). The Lorentz force PIC module will be used to study the effects of energetic ions on stability and confinement of FRC's. We will present 3D visualization using VisIt\footnote{https://wci.llnl.gov/codes/visit/} of the equilibrium trajectories that reveal surprising order. Visualization of the equilibrium trajectories of energetic ions reveal geometric features analogous to closed flux surfaces but with more complex morphologies. We also present linear simulations of energetic ion effects on the tilt stability of the FRC. These initial simulation results will examine the successes and shortcomings of the implementation and possible paths to improvements. We conclude with some remarks on potential application of the full Lorentz PIC and its impact on tokamak simulations.   

Recent Results of ICC Experiment Simulations by the PSI-Center

The Plasma Science and Innovation Center (PSI-Center - http://www.psicenter.org) performs simulations of collaborating Innovative Confinement Concept (ICC) experiments. Collaborators include the Bellan Plasma Group (Caltech), CTH (Auburn U), FRX-L (Los Alamos National Laboratory), HIT-SI (U Wash - UW), LDX (M.I.T.), MST {\&} Pegasus (U Wisc-Madison), PHD (UW), PFRC (PPPL), SSX (Swarthmore College), TCS (UW), and ZaP (UW). Modifications have been made to the NIMROD, HiFi, and PSI-Tet codes to specifically model these ICC experiments, including mesh generation/refinement, appropriate boundary conditions (external fields, insulating BCs, etc.), and kinetic and neutral particle interactions. Output files from these codes are interfaced to the powerful 3-D visualization program, VisIt (http://www.llnl.gov/visit). Results from these simulations, as well as an overview of the Interfacing Group status will be presented.   

Multi-Block Development and Applications of HiFi

Recent improvements to the 3D high-order finite (spectral) element HiFi code include allowing for multiple structured domain blocks to be included as one computational domain. The blocks themselves must be structured, but the collection of blocks can be unstructured. This improvement now allows for much more complex and interesting domains to be modeled including body-fitted, and non-simply connected 3D geometries. Using this new ability in the HiFi code, applications of both the ZaP z-pinch experiment and the HIT-SI experiment are possible. Preliminary MHD plasma solutions with these new geometries will be presented. Additionally in these cases the geometries will have distortions in their elements, which can yield significant errors in field solutions. Mesh metrics are used to correlate the solution error and predict solution error magnitudes.   

Development of a Spectral Element Multigrid Solver for Extended MHD

We report on the development of a Spectral Element Multigrid (SEMG) method as a scalable parallel solver for the 2D HiFi extended MHD code, using high-order modal basis functions on a logically rectangular grid. Coarsening and refining operations transfer the solution between higher and lower polynomial degrees within each grid cell, which is particularly simple for the nested subspaces of modal basis functions. The coarsest-level solver is SuperLU\_dist, which is very efficient because of the reduced problem size. This is accessed through the PETSc library, which could be used in the future to easily explore other options. The key to successful operation is the smoother. It is well-known that the Jacobi smoother is very efficient for the Laplacian discretized with nodal spectral elements because the matrix is diagonally dominant. We have developed a method to exploit this by efficiently transforming between modal and nodal representations. Physics-based preconditioning is used to transform the extended MHD equations to diagonally-dominant form. Scaling tests will be presented for an extended MHD problems.   

Lacunae-based open boundary conditions for dissipative MHD

Hyperbolic-based open boundary conditions have proven to be inadequate for modeling dissipative MHD systems, especially when diffusive effects are dominant at the boundary, as is common, for example, at the ends of an FRC or a mirror plasma. Lacunae-based open boundary conditions (LOBC) are under development for modeling open boundaries in mixed hyperbolic-parabolic systems. Initial work on Lacunae-based BC was done by V.S. Ryaben'kii, S.V. Tsynkov et al. [1]. Lacunae are still regions behind trailing fronts that exist in wave-type solutions. To implement LOBC, a buffer region is appended to the domain of interest. In this buffer region, by taking advantage of the lacunae in the solution, outgoing waves are damped and reflection is prevented. Diffusive behavior is bounded by a Dirichlet or Neumann condition at the edge of the buffer region. Wave reflection is prevented and parabolic behavior is properly bounded. Progress developing LOBC in the SEL/HiFi spectral element code is presented.\\[4pt] [1] V.S. Ryaben'kii et al., Global discrete artificial boundary conditions for time-dependent wave propagation, J. Comp. Phys., 174 (2001) 712   

Gyrofluid model implementation using the 2DX eigenvalue code

The 2DX code is a linear eigenvalue solver primarily designed to solve fluid models of plasma instability in the boundary region of a diverted tokamak. Since kinetic effects are significant for many important instabilities in the plasma edge and scrape-off layer, extending the capabilities of the code to include such effects is desirable. To address this issue, we examine several gyrofluid models using 2DX. The inherent flexibility of the 2DX equation parser allows this to be done in a relatively straightforward manner. The principal complication arises from the presence of integral operators in many gyrofluid models. This can be addressed by approximating integral operators as differential operators by a variety of methods. In addition, we will also report on ongoing benchmarking and physics applications of 2DX using conventional fluid models. Work supported by the U.S. DOE under grant DE-FG02-07ER84718.   

DSC -- Disruption Simulation Code for Tokamaks and ITER applications

Arguably the most important issue facing the further development of magnetic fusion via advanced tokamaks is to predict, avoid, or mitigate disruptions. This recently became the hottest challenging topic in fusion research because of several potentially damaging effects, which could impact the ITER device. To address this issue, two versions of a new 3D adaptive Disruption Simulation Code (DSC) will be developed. The first version will solve the ideal reduced 3D MHD model in the real geometry with a thin conducting wall structure, utilizing the adaptive meshless technique. The second version will solve the resistive reduced 3D MHD model in the real geometry of the conducting structure of the tokamak vessel and will finally be parallelized. The DSC will be calibrated against the JET disruption data and will be capable of predicting the disruption effects in ITER, as well as contributing to the development of the disruption mitigation scheme and suppression of the RE generation. The progress on the first version of the 3D DSC development will be presented.   

Confinement studies for novel MCF reactor configurations

Motivated by ideas from plasma theory, we use a suite of coupled plasma physics codes to explore the confinement performance of a range of tokamak configurations. The codes include GS2, Gryffin, Trinity and TOQ.   

Adaptive Multiscale Electromagnetic Particle Simulations

Hybrid (massless fluid electrons, kinetic ions) and full electromagnetic PIC simulations have recently emerged as powerful computational tools for predicting energetic particle transport in large-scale plasma configurations. Multiple time and length scales associated with plasma and magnetic field inhomogeneities put severe restrictions on the timestep and mesh resolution in these applications. We present two approaches intended to relieve these issues. An asynchronous hybrid code, HYPERS discards traditional time stepping in favor of Discrete-Event Simulation (DES). DES adaptively selects time increments for individual particles and local electromagnetic fields by limiting their per-update changes. HYPERS has been designed to simulate 3D compact fusion devices (such as the SSX experiment at Swarthmore) and interactions of streaming plasmas with obstacles. To validate this new code, we compare results from 2D HYPERS simulations with those obtained with a traditional (time-stepped) hybrid code. We also discuss a novel subgridding (EMPOWER) algorithm for full EM-PIC simulations and demonstrate its efficiency on test problems. Both codes are being geared towards peta/exa-scale computer architectures. We report our undergoing efforts on developing efficient dynamic load-balancing strategies for parallel production runs.   

MHD and 2-Fluid Stability of DIII-D Shot \#96043 using the NIMROD Code

DIII-D shot \#96043 exhibits sawtooth free periods during NB/RF heating. These periods are terminated by ``giant sawtooth'' crashes. This discharge has formed the basis for computational evaluation of the Porcelli model [1]. We have begun [2] to use this discharge in a verification and validation campaign for energetic particle model the NIMROD code [3]. The ability to perform and understand resistive and extended MHD computations is necessary for a proper V \& V study of the energetic particle model. At t=1900 msec, unstable modes are the 1/1 ideal kink mode, a resistive 2/2 mode and a number of high-n localized rippling modes with $q \sim 3$ (near the separatrix). With resistive MHD the high-n modes can be stabilized by a combination of viscosity profile and anisotropic thermal conductivity. When 2-fluid are introduced new high-n localized mode appear. Linear results for all models and nonlinear results for resistive MHD are presented.\\[0pt] [1] M. Choi, A. D. Turnbull, V. S. Chan, et al., Phys. Plasmas 14, 112517 (2007). [2] D. D. Schnack, et al., Bull. Am. Phys. Soc. 54, paper S1.00056 (Abstract Only) (2009). [3] C. C. Kim and the NIMROD Team, Phys. Plasmas 15, 072507 (2008).   

JET Snake Magnetohydrodynamic Equilibria

A long-lived density perturbation labelled a ``snake'' has been observed in the JET tokamak with pellet injection for toroidal field $B_t=3.1T$ and toroidal current $I_t=3MA$.\footnote{R.~D.~Gill {\em et al.}, Nucl.~Fusion \textbf{32} (1992) 723.} Spontaneous snakes triggered by core impurity accumulation have also been reported at $B_t=2.8T$ and $I_t=4.2MA$.\footnote{ibid.} We compute model magnetohydrodynamic equilibria with the 3D ANIMEC code\footnote{W.~A.~Cooper {\em et al.}, Comput.~Phys.~Commun.~\textbf{180} (2009) 1524.} that can recover snake-like conditions by prescribing peaked pressure and hollow toroidal current profiles which are consistent with those in the experimental discharges.\footnote{M.~Hugon {\em et al.}, Nucl.~Fusion \textbf{32} (1992) 33.} The internal helical distortions that look like snake structures have been obtained with the following parameters: $B_t\simeq 2.65T$, $I_t=3.75MA$, $q_0\simeq 1.7$, $q_{min}\simeq 1$, $q_{edge}\simeq 7.5$, $\ell_i\simeq 1.2$, $\left<\beta\right>\simeq 2.4\%$, $\beta_N\simeq 2.3$.   

Free-boundary MHD simulations of time-dependent poloidal flow

In the edge plasma region of tokamak experiments finite toroidal and poloidal flows are routinely observed. MHD theory predicts that when the poloidal velocity is transonic with respect to the poloidal sound speed ($c_{sp} \equiv c_s B_p/B$, where $B_p$ is the poloidal field) transient shocks will develop in the transonic region. Such shocks will then move in the poloidal direction and disappear once they reach the location of the minimum transverse flow cross section. After the end of the transient, a steady-state pedestal in plasma density and pressure is left, with the height of the pedestal depending on the poloidal location. Numerical simulations of fixed-boundary plasmas performed by the authors have confirmed the predictions of theory. In the present work, we extend previous results to include a vacuum region around the plasma, thus studying a more realistic model of experiments. Close to the X-point the poloidal field and poloidal sound speed are vanishingly small. Therefore, the critical poloidal velocity necessary to create the transonic discontinuity in free-boundary simulations with an X-point is much smaller than in the fixed-boundary case. The main result of the free-boundary simulations is to confirm that in realistic conditions steady-state pedestal-like contact discontinuities will form even with small poloidal velocities if the poloidal rotation is transonic near the plasma edge. Work supported by US Department of Energy Contract No.~DE-FG02-93ER54215.   

Analytical and numerical solutions of a force-free equilibrium with flow

The model of plasma equilibrium in presence of a rigid rotation in toroidal direction and/or in a large aspect ratio approximation with arbitrary poloidal flow is studied for a force-free plasma. With this simplifying assumptions the set of Grad-Shafranov-Bernoulli equations decouples. Assuming further a self-similar solution for the poloidal flow stream function it is possible to find an analytical solution for the problem. This solution is compared with a numerical simulation using the FLOW code [1]. Numerical cases assuming a more general toroidal velocity profile with shear, are also considered. \\[4pt] [1] Guazzotto L, Betti R, Manickam J and Kaye S 2004 \textit{Phys. Plasmas} \textbf{11} 604.   

Numerical Calculation of MHD Equilibria with Poloidal-Sonic Flow and FLR Effects

We have developed a code for calculating MHD equilibria with poloidal-sonic flow and FLR effects in high-beta tokamaks, using an aspect-ratio expansion and the two-fluid model. We show that the equilibrium condition can be expressed in terms of differential equations for the first- and second-order poloidal flux and five free profiles of the first-order poloidal flux. We present results for sample equilibria, illustrating behaviors such as the deviation of pressure contours from the flux surfaces and the criteria for the presence of the ``poloidal-sonic singularity.''   

Toroidal equilibria with flow and pressure anisotropy in high-beta reduced MHD models

Effects of flow, finite ion temperature and pressure anisotropy on equilibrium of high-beta toroidal plasmas are investigated based on reduced magnetohydrodynamic (MHD) models. A set of reduced equilibrium equations for high-beta tokamaks with toroidal and poloidal flow comparable to the poloidal sound velocity has been formulated from two-fluid MHD equations with ion finite Larmor radius (FLR) terms and pressure anisotropy. This set of equations has been solved analytically in the limit of single-fluid MHD. The solution shows that the magnetic structure is modified by the flow, the pressure isosurfaces depart from the magnetic flux surfaces due to the poloidal flow indicating transition from sub- to super-poloidal-sonic flow, and anisotropic pressure profiles are self-consistently determined in the presence of flow. We have solved the equilibrium equations for two-fluid equilibria numerically by using the finite element method. We have obtained the following feature of two-fluid equilibria both analytically and numerically: the isosurfaces of the magnetic flux, the pressure and the ion stream function do not coincide with each other.   

Plasma equilibrium with fast ion anisotropy and toroidal flow

Strong induced toroidal flow is typical for present day plasmas with significant anisotropic pressure of energetic ions population. We present a model for the equilibrium solver to account for the fast ion phase space anisotropy and toroidal plasma flow. Anisotropic pressure tensor is computed based on the set of the basis functions used to evaluate the contribution of the fast ions to the pressure tensor. A procedure to include fast ion distribution via the pressure coupling scheme into the Grad-Shafranov equation is discussed. Proposed model allows to include finite orbit width effects self-consistently. We show that in the particular case of zero orbit width any distribution function can satisfy the solubility requirements for Grad-Shafranov equation, which follows from the force balance along the magnetic field lines. For efficient solution technique we developed a conforming grid in the phase space which allows for accurate treatment of the topological boundaries (often characterized by the singularities in particle drift frequencies) in the particle confinement domain.   

Multi-ion equilibrium with strong rotation

We describe a new formulation of the multiple ion species, quasi-neutral, axisymmetric equilibrium problem which includes the possibility of strong (sonic or supersonic) rotation about the geometric axis. This new work is more applicable to well confined, hot plasmas. In contrast to previous related work [1.2] which considered steady states with arbitrary isentropic mass flow, we impose the physically more realistic constraints of uniform temperature and negligible poloidal mass flow. It is shown that there exist three surface functions which are related by a single ordinary differential equation (per species), leaving two surface functions per species. These may be taken to be $T$ and $\Omega$ for each species. Equilibria have been obtained by the LR{\_}eqMI code which simultaneously solves a set of 2+3$ N_{i}$ (where $N_{i}$ is the number of ion species) nonlinear equations at each point, along with Ampere's law and very flexible boundary conditions. Along with the derivation of the model and profiles, some examples of D-T low aspect, elongated tokamak equilibria with and without strong toroidal rotation are given. \\[4pt] [1] L. C. Steinhauer, \textit{Phys. Plasmas} \textbf{6}, 2734 (1999). \\[0pt] [2] J. P. Goedbloed, \textit{Phys. Plasmas} \textbf{11}, 81 (2004).   

Particle distribution modification by magnetohydrodynamic modes

It is known that low amplitude magnetohydrodynamic (MHD) modes can produce modification of high energy particle distributions, and also significant losses.\footnote{R. B. White, N. Gorelenkov, W. W. Heidbrink, and M.A. Van Zeeland {\em Plasma Physics and Controlled Fusion}, 52 045012 (2010)} This phenomenon is important particularly for the redistribution of alpha particle distributions in burning plasmas. Methods are examined for predicting the stochastic onset of large scale transport of a high energy particle distribution in tokamak plasmas due to a spectrum of MHD modes. The phase space of particle orbits is modified by resonant modes by the production of islands in which particles are trapped in the wave. When these islands overlap stochastic trajectories are made possible leading to large scale motion of the particles. Predicting the location and extent of the resonant islands and stochastic domains can lead to a rapid understanding of the proximity of global avalanche.   

TAE-particle interaction in toroidal plasma confinement devices

A model is constructed for the examination of the interaction of a spectrum of low amplitude modes with a high energy particle distribution in a toroidal plasma confinement device. It is shown that mode amplitudes and particle profiles can exhibit periodic oscillations about the mode amplitude threshold for induced stochastic transport of the particle population. The coupled system exhibits a time delay for energy transfer from the particle distribution to the mode, and for island induced collisional transport. We perform a general analysis of the coupled equations and find conditions for transition from a stable limit point to a limit cycle. An ordering of the parameters in the equations are used to examine the period and amplitude of the oscillations in the limit cycle. Analytic results are compared with with numerical integration of the equations, and with simulations of Toroidal Alfven modes interacting with beam particles.   

Simulation Model of Rapid TAE Chirping

Spontaneous nonlinear coherent frequency chirping structures can arise due to the resonant interaction of energetic particles with a discrete toroidal Alfven eigenmode (TAE). The initial development of a coherent structure is quantitatively described by a now standard hole-clump chirping theory. However, it is still unclear what conditions are needed for the TAE chirping frequency to deviate far from the bulk plasma eigenfrequency and enter the Alfven continuum. In our model, the linear TAE controlling equation is derived from the Berk-Mett quadratic form. The interaction is studied with the linear wave with the nonlinear response of energetic particles. For the present study we simplify the wave to a single symmetric couplet while a two-dimensional distribution is used to describe the energetic particles. In order to resolve the fine structure in the phase space, the numerical scheme integrates the Vlasov equation in the Fourier transformed phase space using a method developed by Breizman and Petviashvili. The simulation results show the saturated wave amplitude and square root law of the initial chirping are in accord with previous theory. We have found conditions where the chirping signal enters the Alfven continuum and a larger amplitude and more rapidly chirping signal then develops. Plots of the phase space structure can reproduce the shape of the separatrix structure that partitions the trapped and passing particles. We attempt to relate the portrait of the phase space structure with the measured wave amplitude and chirping frequency.   

Gyrokinetic particle simulations of reversed shear Alfv\'en eigenmode excited by antenna and fast ions

Global gyrokinetic particle simulations of reversed shear Alfv\'en eigenmode (RSAE) have been successfully performed and verified. We have excited the RSAE by initial perturbation, by external antenna, and by energetic ions. The RSAE excitation by antenna provides verifications of the mode structure, the frequency, and the damping rate. When the kinetic effects of the background plasma are artificially turned off, the mode excited by antenna shows a structure and a frequency similar to the theoretical calculation and the mode amplitude shows a near-linear growth. When kinetic thermal ions are added in, the mode amplitude eventually saturates due to the ion Landau damping. The damping rate is measured from the saturation level. The RSAE excited by fast ions shows an exponential growth. Comparing to the antenna excitation, the mode structure and the frequency are modified by the fast ions. With kinetic thermal ions, the mode frequency increases due to the raise of the Alfv\'en continuum, while the mode structure has no significant change. The results are benchmarked with XHMGC simulations and good agreements are obtained.   

Use of high order, periodic orbits in the PIES code

We have implemented a version of the PIES code (Princeton Iterative Equilibrium Solver\footnote{A. Reiman \textit{et al}~2007 \textit{Nucl. Fusion} \textbf{47} 572}) that uses high order periodic orbits to select the surfaces on which straight magnetic field line coordinates will be calculated. The use of high order periodic orbits has increase the robustness and speed of the PIES code. We now have more uniform treatment of in-phase and out-of-phase islands. This new version has better convergence properties and works well with a full Newton scheme. We now have the ability to shrink islands using a bootstrap like current and this includes the m=1 island in tokamaks.   

Algorithm for Calculating the Time Evolution of a Neoclassical Tearing Mode Using an Electrostatic Gyrokinetic Code coupled to a 3D Equilibrium Solver

We present an algorithm for calculating the time evolution of a neoclassical tearing mode as it passes through a sequence of equilibria by coupling the PIES 3D equilibrium code to an electrostatic gyrokinetic code. The key is the observation that by working in the Coulomb gauge it is possible to reduce the solution for the inductive component of the electric field to the solution of a 3D Poisson equation for the gauge function. This equation can be solved using the existing capability in the PIES code for solving the 3D Poisson equation. It is also notable that the gyrokinetic code can be used to incorporate kinetic and flow effects, as well as the effects of electrostatic turbulence, in the equilibrium solutions. This is the case because the PIES code solves the equilibrium equations in the form $\nabla \times $\textbf{B} = \textbf{j}(\textbf{B}), where \textbf{j}(\textbf{B}) is a nonlinear function that determines the equilibrium current density, \textbf{j}, in the presence of a given field, \textbf{B}. The additional physics can be incorporated by calculating \textbf{j}$_{\bot}$ directly from a pullback transformation of the drift velocities, using four-point averaging. The bootstrap current calculated by the gyrokinetic code can be self-consistently incorporated as the constant of integration for the equation determining $j_{\vert \vert}$.   

Improvement of the numerical matching technique for resistive MHD stability analysis

We have developed a new numerical matching technique for linear stability analysis of resistive MHD modes [1]. This technique utilizes an inner layer with a finite width, which is in contrast to the asymptotic matching where the inner layer is taken to be infinitely thin. This singular nature of the asymptotic matching introduces some practical difficulties. For example, the accurate numerical calculation of the so-called matching data is not easy. In the new matching technique, we solve the MHD equation including (excluding) plasma inertia and electrical resistivity in the inner layer (outer region) as in the asymptotic matching. However, those difficulties are removed since we do not need to tackle the singularity head-on if the inner-layer width is finite. In this study, we improve our technique by correcting the outer-region solution in a successive manner, where the plasma inertia and resistivity are taken into account. The ideal MHD solution in the previous study [1] serves as the zeroth-order solution.\\[4pt] [1] M. Furukawa, S. Tokuda and L. -J. Zheng, Phys. Plasmas vol.17, 052502 (2010).   

Kink-tearing mode conversions with current interchange and small parallel ion velocity effects taken into account

The conversions of kink type of modes, such as $n=1$ internal kink mode, RWMs, etc., to tearing modes are widely observed experimentally. In this presentation we explain these conversions using the theory of newly discovered current interchange tearing modes [CITMs, Zheng and Furukawa, Phys. Plasmas {\bf 17}, 052508 (2010)], with the kinetic enhancement of parallel inertia by the so-called small parallel ion velocity effect [SPIV, Zheng and Tessarotto, Phys. Plasmas 3, 1209 (1996)] taken into account. Interchange-type (i.e., kink) modes exchange not only thermal and magnetic energies, but also current, between flux tubes, so that current sheet can be formed at mode rational surfaces and kink type of modes are converted to tearing type of modes. It is pointed out that, when the so-called SPIV inertia enhancement is taken into account, the current interchange effect becomes the dominant driving force for field line reconnection. The underlying physics will be explained intuitively. Both analytical and numerical results will be presented. Extension of AEGIS code to study the kink-tearing mode conversion processes will also be discussed.   

Nonlinear dynamics of multiple NTMs in tokamaks

The nonlinear evolution of two coupled neoclassical tearing modes (NTMs) is investigated through numerical simulations using a 3D toroidal code based on a set of generalized reduced MHD equations. The parametric interaction of the 2/1 and 3/1 modes is seen to result in the excitation of low frequency oscillations in the range of acoustic frequencies. The GAM like oscillations manifest themselves as oscillations in the energies of the NTMs and their origin is traced to the presence of the finite neoclassical electron stress tensor contribution in the Ohm's law. This contribution has the effect of making the flow energies of the modes to become larger than the magnetic energies of the modes and the perpendicular flow patterns to spread out from the mode resonant surfaces. Such an expanded flow pattern is seen to be responsible for the effective coupling between the two modes despite their resonance surfaces being quite apart. The physical implications of this novel coupling mechanism on the saturated amplitudes of the NTMs and their relevance to some recent experimental results are discussed.   

An analysis of the evolution of two coupled neoclassical tearing mode islands

It has long been experimentally observed that two neoclassical tearing mode islands resonant at different magnetic surfaces tend not to coexist. To address this, we describe the temporal evolution of each magnetic island width using the modified Rutherford equation (MRE). This equation can be obtained by integrating Ampere's law across a magnetic island region in a radially infinite cylindrical plasma. Ohm's law is used to express the polarization, curvature and neoclassical effects on the island evolution. But in experiment, the geometry and equilibrium profiles of the evolving system impose linear drive terms that differ for each magnetic island. Also, the islands are coupled through their perturbations. Both effects alter the evolution of the island widths dramatically. In this work, we develop a two island MRE code with accurate linear drive terms and coupled effects for both islands. With this code we investigate how these couplings could explain the noted experimental observations.   

Comparison of energetic particles effects on $m/n=3/2$ and $m/n=2/1$ modes in DIII-D

Experimental tokamak discharges commonly include an evolving $m/n=3/2$ mode before a $2/1$ mode onset, leading to termination of the discharge. The ideal limit of $n=2$ is generally higher than the $n=1$ in $\beta _{N}$, though the $3/2$ mode typically onsets when the rational surface comes into existence off axis in reversed shear, and then evolves in a nonlinear state. All the while energetic particles are affecting both modes differently. Using an experimental equilibrium reconstruction from a hybrid DIII-D discharge with $q_{min}>\sim $1, a linear resistive stability analysis is presented in this stage. The 3-D resistive MHD code NIMROD coupled to a $\delta f$ PIC model for the energetic particles is used to study the kinetic effects of the particles on the \textit{n=1 and n=2} modes. The linear growth is calculated at various $q_{min}$ and $\beta _{N}$ ranging from the resistive unstable to the ideal unstable regime. Results show the interaction of the particles with the non-resonant response on axis causes destabilization of modes as opposed to a damping effect previously reported in the higher $q_{min}$ cases.   

Toroidal Coupling of Tearing Modes in RFP

Strong ion heating and plasma momentum transport are observed during periodic magnetic relaxation events in the Madison Symmetric Torus (MST) RFP experiments. Two types of tearing modes are responsible for impulsive reconnection: m =1 modes in the plasma core and m = 0 edge resonant modes. Their coupling can be caused by toroidal effects or nonlinear interaction. In order to distinguish these two mechanisms we investigate the spatial structure of the core and edge resonant tearing modes in the toroidal geometry using the initial value code NIMROD. Substantial toroidal asymmetry is found at the MST aspect ratio R/a =3 for the edge resonant mode. The asymmetry is strong for the radial component, B$_{r}^{(inboard)}$/ B$_{r}^{(outboard) }\sim $ 8, and less significant for the poloidal and toroidal components ($\sim $1.5-2). The use of the linear version of NIMROD is justified by noting that slowly varying magnetic perturbations have robust spatial structure which is weakly sensitive to the mechanism -- linear or nonlinear -- of the mode excitation. These arguments are confirmed by good agreement with the experimental profiles.   

Nonlinearly unstable interchange modes in transverse magnetic field

We study the ideal interchange instability in a plasma immersed in a constant transverse field near marginal stability. Using reduced equations for a strong axial field, we investigate the tradeoff between the deviation from marginality and residual convection. We calculate a method to predict $|\vec{B}_\perp- \vec{B}_{crit}|$, the deviation of the field from marginality, as a function of residual convective flux. Such a formulation would find application in assessing the B-field tolerances in stellarator coil design. We use an expansion in small perturbations in the field amplitude about marginality to find nonlinear analytic solutions. The lowest order expansion yields an eigenvalue equation for the critical field for marginal stability, $\vec{B}_{crit}$. A time-evolution equation for the amplitude is found from the third order expansion. Simplifying this result for $kL\gg 1$, we find that the system is nonlinearly unstable for perturbations larger than a critical value proportional to the square root of the deviation. Nonlinear numerical simulations of this system in dissipative MHD have verified the result in our calculations. Our results and method are also compared with previous works by Beklemishev, Cowley, and Waelbroeck. Work supported by the USDOE.   

Nonlinear $g$ Mode Theory in Extended MHD

Two-fluid (2F) and finite Larmor radius (FLR) effects can modify instability growth rates and relaxation physics of many macroscopic processes in high temperature plasmas. The dominant order of these effects can be captured by extended MHD models that include generalized Ohm's law and a gyroviscous stress tensor. Whereas these nonideal effects tend to stabilize linear growth of $g$ modes with large perpendicular wavenumber, their influence on nonlinear $g$ mode physics is not well understood. Previously, an analytic solution was found describing the intermediate nonlinear phase of the interchange-like modes in an ideal MHD model. In the present work, we address the question how the ideal intermediate nonlinear phase would be altered by the 2F and FLR effects. We develop an analytic theory for intermediate nonlinear $g$ mode growth in an extended MHD model. The non-dissipative nature of 2F and FLR effects allows the construction of a theory that is based on conservation constraints using a Lagrangian framework. In particular, an electron fluid displacement ${\mbox{\boldmath $\xi$}}_e$ is introduced in addition to the ion fluid displacement ${\mbox{\boldmath $\xi$}}$. The displacements of the two fluids are related through the plasma current. The magnetic flux is conserved following the electron fluid motion ${\mbox{\boldmath $\xi$}}_e$. The Lagrangian theory has recovered the 2F and FLR effects on linear $g$ modes previously obtained from Eulerian theory. Progress on the nonlinear analytic results will also be presented and discussed.   

The effect of three dimensional flux surface shaping on ideal ballooning stability

An understanding of how 3-D shaping of MHD equilibria affects highly localized instabilities is an attractive goal for the optimization of non-axisymmetric magnetic confinement devices. The use of 3-D resonant magnetic perturbations to suppress edge localized modes in tokamak experiments also motivates a detailed study of the ballooning stability properties of nearly axisymmetric equilibria. Understanding the basic role of 3-D shaping is difficult due to the computational cost and complexity associated with the calculation of global 3-D MHD equilibria. Numerical implementation of local 3-D equilibrium theory is used to generate sets of equilibria where flux surface shape is explicitly specified by 3-D parametrizations. The effects of 3-D shaping on geometric quantities of interest to local mode stability is examined. Marginal stability diagrams are used to analyze ballooning stability properties of shaped stellarator equilibria and nearly axisymmetric tokamak equilibria. Implications for ELM properties in the presence of 3-D resonant magnetic perturbations will be discussed.   

Edge instabilities in toroidal fusion plasmas

Magnetically confined fusion plasmas (tokamaks and spherical torii) can achieve good central confinement by operating in H-mode, using a D-shaped plasma cross-section with a large local pressure gradient at the plasma boundary. Fast electromagnetic instabilites destabilized by the pressure gradient range from large episodic Edge Localized Modes (ELMs) to smaller continuous oscillations; sometimes instability can be completely suppressed. Previous MHD simulations at realistic or near-realistic resistivity, with the M3D code, have shown[1] that large ELMs can drive asymptotic magnetic field splitting around the plasma separatrix, creating a chaotic magnetic tangle in the outer part of the plasma that has important nonlinear effects on the ELM, including on nonlinear growth rates. Additional phenomena, such as plasma toroidal rotation and two-fluid processes, are found to have significant linear and nonlinear effects on the stability and dynamics of both large ELMs and smaller continuous oscillations. Toroidal rotation can be stabilizing and can partially shield the edge perturbation from the plasma interior, as it does for magnetic stochasticity due to applied nonaxisymmetric fields. \\ \leftline{[1] L. Sugiyama and H.R. Strauss \emph{Phys. Plasmas} \textbf{17} 062505 (2010).}   

Transport and MHD simulations of intrinsic and pellet induced ELMs

Verification of ELM mechanism and demonstration of ELM control are important issues in current fusion researches targeting ITER and DEMO. This work investigates the physics and operational characteristics of intrinsic and pellet induced ELMs throughout transport simulations using 1.5 D transport codes (C1.5/ASTRA) and MHD simulations using M3D code. Transport simulations are focused on prediction of the global parameters such as ELM energy loss in the type-I ELMy H-mode discharges with and without pellet pace making to examine an applicability of pellet injection for ELM mitigation in KSTAR and ITER. On the other hand, MHD simulations are conducted to explore the physics of intrinsic and pellet induced ELMs by applying the artificial free energy sources of velocity stream and density perturbations on the marginally stable equilibrium, respectively. Similarities and differences of triggering phenomena between intrinsic and pellet induced ELMs are discussed from the MHD approach.   

Global Geodesic Acoustic Modes in Tokamak Plasmas

Global Geodesic Acoustic Modes (GGAM) in Tokamak Plasmas are investigated in the framework of reduced ideal MHD. The axisymmetric eigenvalue problem for perturbed pressure and electrostatic potential is formulated as a recurrent set of equations for poloidal Fourier harmonics. For uniform safety factor q and temperature profile with a maximum at radius $r=r_0 \neq0$ the analytical solution of this eigenvalue problem is obtained for a truncated set of equations taking into account the $m=0$ and $m=2$ poloidal harmonics of potential and the $m=1 $ harmonic of pressure. This solution exists in wide range of $\beta q^2$. It is shown both analytically and numerically that the higher harmonics of pressure ($m=3$) and electrostatic potential ($m=4$) reduce the range of the parameters, in which GGAM exist, due to the resonance with continuum spectrum. The domain of GGAM existence in the ($\beta q^2$, $r_0$)-plane is represented. Higher poloidal harmonics ($m>4$) are shown to weakly affect the GAM spectrum and do not lead to the appearance of other global eigenmodes. The work is supported in part by grant RBRF 10-02-01302 and by Ministry of Education and Science of the RF, contract 1.5-508-008-045.   

Error-Field and Resistive Wall Coupling in NIMROD

Boundary conditions for a periodic cylinder that allow for the simultaneous presence of a resistive wall and external error fields have been successfully implemented in \textsc{nimrod}. Small magnetic field errors stemming from coil feeds and misalignment are present in all devices. These errors are modeled as small helical currents at some radius outside the resistive wall, which contribute terms to the \textsc{nimrod} boundary condition at the wall. Using these new \textsc{nimrod} capabilities, error-field penetration is studied for intrinsically stable rotating plasmas. An axial equilibrium flow is included in the simulation in order to observe suppression of error-field driven modes by rotation. Error-fields of a critical amplitude penetrate the plasma and create stationary magnetic islands. These numerical results are compared to the analytic predictions of Fitzpatrick [Nucl. Fusion \textbf{33}, 1049 (1993)] for periodic cylinder geometry and visco-resistive plasmas. Further generalization of the resistive wall and error-field boundary conditions in \textsc{nimrod} to toroidal geometry will be discussed.   

Including a finite element option in the VACUUM code

One aspect of the VACUUM code\footnote{M.~S~.Chance, Phys. Plasmas \textbf{4} (6), June 1997.} is its legacy Fourier analysis in the poloidal variable, $\theta$, of the fields, which owed its origin to its compliance with the linear stability codes at PPPL. This may not be the optimum representation for modeling the modes currently observed in experimients and simulations. Furthermore, at present, for interfacing to the finite elements representation of say, M3D and M3D-C1, the inverse Fourier transform has to be taken to a discrete space. To alleviate these potentially numerical and representational problems, VACUUM is upgraded to include a finite elemnet option. These are piecewise constant functions in $\theta$. As in the Fourier method, care must be taken when addressing the singularities that is intrinsic to the Green's function technique that is used.   

A Sharp Boundary Model of Nonaxisymmetric Vertical Disruption Events in Tokamaks

A semi-analytic sharp boundary model of a nonaxisymmetric vertical disruption event (VDE) in a vertically elongated tokamak plasma is developed. The model is used to simulate nonaxisymmetric VDEs with a wide range of different plasma equilibrium and vacuum vessel parameters. These simulations yield poloidal halo current fractions and toroidal peaking factors that are similar to those seen in experiments. The simulations also reproduce the experimentally observed inverse scaling between the current fraction and the peaking factor. The peak poloidal halo current density is found to correlate strongly with the reciprocal of the minimum edge safety-factor attained during the disruption. The peak vertical force per unit area acting on the vacuum vessel is observed to have a strong correlation with the equilibrium toroidal plasma current at the onset of the disruption, but is also seen to increase with increasing vacuum vessel conductivity relative to the SOL plasma. Finally, the peak horizontal force is found to be largely determined by the plasma beta prior to the disruption.   

Observation of Fast Plasma Convection During Disruptions In Tokamak T-11M

We investigate fast cross-field plasma convection during disruptions in tokamak T-11M with a lithium limiter. The process of the lithium penetration into the plasma core is used as a marker for identification of the bulk plasma dynamics. The distribution of the impurities is obtained from an AXUV multichannel detector array that measures total radiation of the lithium ions in the process of their penetration from the limiter to the hot plasma region. Fast and deep lithium penetration into the plasma core during disruption events has been reported earlier [1]. The analysis of the previous experiments and the new experimental results allows us to determine important distinctions of the lithium behavior for the cases of minor and major disruption events in the T-11M tokamak. The key element of these differences is the depth of the lithium penetration to the plasma center during disruption development. The results can be useful for modeling and mitigation of the disruption events in tokamaks. [1] A.G. Alekseev, A.M. Belov, E.A. Azizov et al., ``Studies of fast penetration of impurities into core plasma during the disruption at T-11M'', 26$^{th}$ EPS Conf. on Cont. Fusion and Plasma Phys., Maastricht, Netherlands, P2.072 (1999).   

Control of ideal and resistive magnetohydrodynamic modes in reversed field pinches with a resistive wall

Numerical studies of magnetohydrodynamic (MHD) instabilities with feedback control in reversed field pinches (RFPs) are presented. Specifically, investigations are performed of the stability of $m = 1$ modes in RFPs with control based on sensing the normal and tangential magnetic field at the resistive wall. The control scheme is based on that of [Finn, Phys. Plasmas 13, 082504 (2006)], which is here modified to use a more realistic plasma model. The plasma model now uses full resistive MHD rather than reduced MHD, and it uses two realistic classes of equilibrium parallel current density profiles appropriate to RFPs. Results with these modifications are in qualitative agreement with [Finn, Phys. Plasmas 13, 082504 (2006)]: the feedback can stabilize tearing modes (with resistive or ideal wall) and resistive-wall ideal modes. The limit for stabilization is again found to be near the threshold for ideal modes with an ideal wall. In addition to confirming these predictions, the nature of the instabilities limiting the range of feedback stabilization near the ideal-wall ideal-plasma threshold are studied, and the effects of viscosity, resistive wall time, and plasma resistivity are reported.   

Active Feedback Stabilization of Mirror Trap -- Experimental Investigation

Plasma confinement in axi-symmetric mirror machine is unstable to large-scale `flute' perturbations. Since the spatial scale of the perturbations is comparable to the plasma radius, and the time scale is 10-100 $\mu $s, it might be possible to suppress the instability using external active feedback. About 40 years ago several feedback experiments demonstrated some improvement in confinement, but the slow electronics of that time limited the feedback effectiveness. Since then there has been great improvement in feedback theory, plasma simulation, and digital real-time systems. As a result, active feedback is gradually becoming a major tool in toroidal confinement machines. We try to re-examine the physics of feedback stabilization of mirror machines using a table-top experiment. For this purpose we have built a small mirror trap and have studied the large scale dynamics of the plasma. The feedback system consists of optical sensors, magnetic or electric actuators, and fast and programmable digital processing system. We will present the instability evolution and open loop response, as measured by the sensors array and fast photography.   

Active Feedback Stabilization of Magnetic Mirror Trap -- Theoretical Investigation

An experimental system is being built in an attempt to stabilize flute instabilities in a mirror machine using active feedback. Using the drift-ordered fluid equations derived in [1], the system is investigated theoretically and numerically. Experimental results are compared with code prediction. Also, different possible methods of feedback stabilization are investigated. These methods include use of electrostatic and magnetic actuators. \\[4pt] [1] A. D. Beklemishev \textit{et al.},``Vortex confinement of plasmas in symmetric mirror traps'', Fusion Science and Technology, Vol. 57, May 2010.   

Energetic particle driven Alfv\'{e}nic instabilities by a kinetic-fluid model

A kinetic-fluid model\footnote{C.Z.Cheng and J.R.Johnson, J. Geophys. Res. {\bf 104}, 413 (1999).} is successfully implemented into a massively parallel numerical simulation code. Excitation of TAE mode in a tokamak geometry is demonstrated.\footnote {Y.Nishimura and C.Z.Cheng J. Plasma and Fusion Research Series {\bf 9}, (2010).} The kinetic-fluid model incorporates all the particle dynamics through the pressure tensor by taking the second order moment of the particle simulation while the electromagnetic field quantities are evolved in the fluid equations. Continuing efforts on the development of the model are reported. The key elements are the treatment of kinetic electrons, shaped geometry, and high beta plasma application. The similarity and the difference (in gyrokinetic Poisson equation) between electromagnetic gyrokinetic simulation models are discussed. This work is supported by National Cheng Kung University Top University Project.   

Evidence of a 100 cm Plasma in the ZaP Flow Z-Pinch

The ZaP Flow Z-pinch experiment at the University of Washington investigates the effect of sheared flows on MHD stability. Evidence will be presented showing that an axially flowing Z-pinch plasma is produced that is 100 cm long with a 1 cm radius. The plasma remains quiescent for many Alfven and flow time scales. The quiescent periods are characterized by low magnetic mode activity measured at several locations along the plasma column and by stationary visible plasma emission. Profiles of the plasma's axial flow are measured with a multi-chord ion Doppler spectrometer. A sheared flow profile is observed to be coincident with the quiescent period. The flow profile is well-understood and consistent with classical plasma viscosity. Plasma lifetime appears to only be limited by plasma supply and current waveform. Equilibrium is determined by the following diagnositc measurements: interferometry for density; spectroscopy for ion temperature, plasma flow, and density; Thomson scattering for electron temperature; Zeeman splitting for internal magnetic field measurements; and fast framing photography for global structure.   

Investigation of Heating Mechanisms in the ZaP Flow Z-Pinch

The ZaP Flow Z-Pinch at the University of Washington is a basic plasma physics experiment that investigates stabilizing a Z-pinch with a radially-varying axial flow, dv$_{z}$/dr. ZaP consists of a coaxial accelerator region coupled to a pinch assembly region. It is hypothesized that the primary means of heating in ZaP is through adiabatic compression during pinch formation. The 10 cm inner electrode of ZaP is replaced with a 16 cm inner electrode to investigate this hypothesis. A four-chord HeNe interferometer is used to determine a pinch density profile as a function of time, and radial force balance and conservation of energy equations are used to determine temperature and magnetic field profiles. Temperature measurements are made with a 20-chord imaging spectrometer (T$_{i})$ and a Thomson-scattering system (T$_{e})$ and compared to the calculated temperatures. The profiles are investigated for a range of accelerator densities and pinch currents for both electrode configurations. The possible effects of adiabatic compression, Ohmic heating and shock heating will be evaluated and reported.   

Deconvolution of Stark-broadened Spectra for Multi-point Density Measurements in the ZaP Experiment

The ZaP Flow Z-pinch experiment uses sheared flow to mitigate MHD instabilities. The pinches exhibit Stark broadened emission spectra, which are captured at 20 locations using a multi-chord spectroscopic system. Sufficiently isolated impurity lines with associated instrument effects are well-approximated by a Voigt function. Two methods have been developed to resolve plasma electron density by deconvolving the spectral Voigt profile into constituent functions: Gaussian function associated with instrument effects and temperature, and a Stark effect Lorentzian function associated with plasma density. The first method is a direct least-squares fit while the second method uses analytic Fourier transforms of the constituent functions to fit the Voigt profile in the Fourier domain. The latter method requires fewer fitting parameters and shows promise in being less susceptible to instrumental noise and to contamination from neighboring low-intensity lines. The methods are evaluated and tested using simulated lines and are applied to 229.7 nm C III and 306.3 nm O IV data from multiple chords to determine plasma density across the diameter of the pinch. These density measurements are used to gain a better understanding of Z-pinch equilibrium.   

Internal Magnetic and Temperature Measurements on the ZaP Experiment

The ZaP Flow Z-pinch experiment is studying the effect of sheared flows on gross plasma stability. During a quiescent period in the magnetic mode activity, a dense Z-pinch with a sheared flow is observed on the axis of the machine. A better comparison between the experimental and analytic results can be made once the pressure profile is known. Measurements of the electron temperature on the axis of the Z-pinch are made with a single point Thomson scattering system. The magnetic field is measured at the characteristic radius using Zeeman splitting. These diagnostics have been built using available components, reducing the cost. The local electron temperature is found by including all of the effects of the notch filters in the spectrometer. The local magnetic field is found by deconvolving the spectral intensity of the left and right circularly polarized line emission. The diagnostics, calibration, and analysis techniques will be described. The measurements show that the current is confined to the characteristic radius and that the temperature is consistent with that found using force balance.